Search: id:A054333
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%I A054333
%S A054333 1,11,65,275,935,2717,7007,16445,35750,72930,140998,260338,461890,
%T A054333 791350,1314610,2124694,3350479,5167525,7811375,11593725,16921905,
%U A054333 24322155,34467225,48208875,66615900,91018356,123058716,164750740
%N A054333 1/256 of tenth unsigned column of triangle A053120 (T-Chebyshev, rising 
               powers, zeros omitted).
%C A054333 If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then 
               a(n-10) is the number of 10-subsets of X intersecting both Y and 
               Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
%C A054333 9-dimensional square numbers, eighth partial sums of binomial transform 
               of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+8,i+8)*b(i)}, where b(i)=[1,
               2,0,0,0,...]. [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), 
               Mar 05 2009]
%D A054333 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 795.
%D A054333 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory 
               to algebra and number theory, 2. ed., Wiley, New York, 1990.
%D A054333 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pp. 189, 194-196.
%H A054333 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A054333 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 A054333 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A054333 a(n) = (2*n+9)*binomial(n+8, 8)/9 = ((-1)^n)*A053120(2*n+9, 9)/2^8. G.f. 
               (1+x)/(1-x)^10.
%F A054333 a(n)=2*C(n+9, 9)-C(n+8, 8). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003
%F A054333 a(n)=C(n+8,8)+2*C(n+8,9) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), 
               Mar 05 2009]
%t A054333 s1=s2=s3=s4=s5=s6=s7=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; 
               s6+=s5; s7+=s6; AppendTo[lst,s7],{n,0,7!}]; lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Jan 15 2009]
%Y A054333 Partial sums of A053347. Cf. A053120, A000581.
%Y A054333 Cf. A005585, A040977, A050486, A053347 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 15 2009]
%Y A054333 Sequence in context: A120723 A053367 A163706 this_sequence A036601 A125321 
               A054490
%Y A054333 Adjacent sequences: A054330 A054331 A054332 this_sequence A054334 A054335 
               A054336
%K A054333 nonn,easy
%O A054333 0,2
%A A054333 Barry E. Williams, Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Mar 15 2000.

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