Search: id:A000582
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%I A000582 M4712 N2013
%S A000582 1,10,55,220,715,2002,5005,11440,24310,48620,92378,167960,293930,
%T A000582 497420,817190,1307504,2042975,3124550,4686825,6906900,10015005,
%U A000582 14307150,20160075,28048800,38567100,52451256,70607460,94143280
%N A000582 Binomial coefficients C(n,9).
%C A000582 Figurate numbers based on 9-dimensional regular simplex. - jvospost3(AT)gmail.com 
               (jvospost3(AT)gmail.com), Nov 28 2004
%C A000582 a(n) = -A110555(n+1,9). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 27 2005
%C A000582 Product of 9 consecutive numbers divided by 9! - Artur Jasinski (grafix(AT)csl.pl), 
               Dec 02 2007
%C A000582 In this sequence there are no primes - Artur Jasinski (grafix(AT)csl.pl), 
               Dec 02 2007
%C A000582 With a different offset, number of n-permutations (n>=9) of 2 objects: 
               u,v, with repetition allowed, containing exactly nine (9) u's. Example: 
               a(1)=10 because we have uuuuuuuuuv, uuuuuuuuvu, uuuuuuuvuu, uuuuuuvuuu, 
               uuuuuvuuuu, uuuuvuuuuu, uuuvuuuuuu, uuvuuuuuuu, uvuuuuuuuu and vuuuuuuuuu. 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008
%C A000582 sage: taylor( mul(1/(1-x^2) for i in range(10)),x,0,60)>> solution: 1 
               + 10*x^2 + 55*x^4 + 220*x^6 + 715*x^8 + 2002*x^10 + 5005*x^12 + 11440*x^14 
               + 24310*x^16 + 48620*x^18 + 92378*x^20 + 167960*x^22 + 293930*x^24 
               + 497420*x^26 + 817190*x^28 + 1307504*x^30 + 2042975*x^32 + 3124550*x^34 
               + 4686825*x^36 + 6906900*x^38 + 10015005*x^40 + 14307150*x^42 + 20160075*x^44 
               + 28048800*x^46 + 38567100*x^48 + 52451256*x^50 + 70607460*x^52 + 
               94143280*x^54 +... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 29 2009]
%D A000582 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000582 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000582 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 828.
%D A000582 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 196.
%D A000582 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 
               256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see 
               vol. 2, p. 7.
%D A000582 J. C. P. Miller, editor, Table of Binomial Coefficients. Royal Society 
               Mathematical Tables, Vol. 3, Cambridge Univ. Press, 1954.
%H A000582 T. D. Noe, <a href="b000582.txt">Table of n, a(n) for n=9..1000</a>
%H A000582 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A000582 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A000582 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=259">
               Encyclopedia of Combinatorial Structures 259</a>
%H A000582 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A000582 H. K. Kim, <a href="http://com2mac.postech.ac.kr/papers/2001/01-22.pdf">
               On Regular Polytope Numbers</a>, Journal: Proc. Amer. Math. Soc. 
               131 (2003), 65-75, as PDF file.
%H A000582 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A000582 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A000582 J. V. Post, <a href="http://www.magicdragon.com/poly.html">Table of Polytope 
               Numbers, Sorted, Through 1,000,000</a>.
%F A000582 G.f.: x^9/(1-x)^10
%F A000582 a(n+8)=n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)/9! - Artur Jasinski 
               (grafix(AT)csl.pl), Dec 02 2007, R. J. Mathar, Jul 07 2009
%p A000582 A000582 := n->binomial(n,9);
%p A000582 A000582:=1/(z-1)**10; [S. Plouffe in his 1992 dissertation for offset 
               0.]
%p A000582 seq(binomial(n,9),n=0..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 23 2008, R. J. Mathar, Jul 07 2009
%t A000582 Table[n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)/9!,{n,1,100}] - Artur 
               Jasinski (grafix(AT)csl.pl), Dec 02 2007
%Y A000582 Cf. A053138, A053131, A000581, A035927.
%Y A000582 Sequence in context: A008492 A023035 A128936 this_sequence A145459 A034241 
               A022575
%Y A000582 Adjacent sequences: A000579 A000580 A000581 this_sequence A000583 A000584 
               A000585
%K A000582 easy,nonn
%O A000582 9,2
%A A000582 N. J. A. Sloane (njas(AT)research.att.com).
%E A000582 More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 23 2000
%E A000582 Formulas referring to other offsets rewritten by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 07 2009

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