0,2

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

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]

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.

Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Milan Janjic, Two Enumerative Functions

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].

Index entries for sequences related to Chebyshev polynomials.

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.

a(n)=2*C(n+9, 9)-C(n+8, 8). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003

a(n)=C(n+8,8)+2*C(n+8,9) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]

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]

Partial sums of A053347. Cf. A053120, A000581.

Cf. A005585, A040977, A050486, A053347 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]

Sequence in context: A120723 A053367 A163706 this_sequence A036601 A125321 A054490

Adjacent sequences: A054330 A054331 A054332 this_sequence A054334 A054335 A054336

nonn,easy

Barry E. Williams, Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 15 2000.