0,2

Partial sums of A054333.

If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-11) is the number of 11-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007

10-dimensional square numbers, ninth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+9,i+9)*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.

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+10)*binomial(n+9, 9)/10 = ((-1)^n)*A053120(2*n+10, 10)/2^9.

G.f. (1+x)/(1-x)^11.

a(n)=2*C(n+10, 10)-C(n+9, 9). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003

a(n)=C(n+9,9)+2*C(n+9,10) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]

s1=s2=s3=s4=s5=s6=s7=s8=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; s8+=s7; AppendTo[lst, s8], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]

Cf. A053120, A054333.

Cf. A005585, A040977, A050486, A053347, A054333 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]

Sequence in context: A009405 A009839 A071767 this_sequence A026964 A026974 A109711

Adjacent sequences: A054331 A054332 A054333 this_sequence A054335 A054336 A054337

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)