9,2

Figurate numbers based on 9-dimensional regular simplex. - jvospost3(AT)gmail.com (jvospost3(AT)gmail.com), Nov 28 2004

a(n) = -A110555(n+1,9). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 27 2005

Product of 9 consecutive numbers divided by 9! - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007

In this sequence there are no primes - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007

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

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 196.

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.

J. C. P. Miller, editor, Table of Binomial Coefficients. Royal Society Mathematical Tables, Vol. 3, Cambridge Univ. Press, 1954.

T. D. Noe, Table of n, a(n) for n=9..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 259

Milan Janjic, Two Enumerative Functions

H. K. Kim, On Regular Polytope Numbers, Journal: Proc. Amer. Math. Soc. 131 (2003), 65-75, as PDF file.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.

G.f.: x^9/(1-x)^10

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

A000582 := n->binomial(n, 9);

A000582:=1/(z-1)**10; [S. Plouffe in his 1992 dissertation for offset 0.]

seq(binomial(n, 9), n=0..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008, R. J. Mathar, Jul 07 2009

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

Cf. A053138, A053131, A000581, A035927.

Sequence in context: A008492 A023035 A128936 this_sequence A145459 A034241 A022575

Adjacent sequences: A000579 A000580 A000581 this_sequence A000583 A000584 A000585

easy,nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 23 2000

Formulas referring to other offsets rewritten by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 07 2009