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A057788 Expansion of (1+x)/(1-x)^12. 10
1, 13, 90, 442, 1729, 5733, 16744, 44200, 107406, 243542, 520676, 1058148, 2057510, 3848222, 6953544, 12183560, 20764055, 34512075, 56071470, 89224590, 139299615, 213696795, 322561200, 479634480, 703323660, 1018031196, 1455797448, 2058314440, 2879378332 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

1/2^10 of twelfth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).

If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-12) is the number of 12-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007

11-dimensional square numbers, tenth partial sums of binomial transform of [1,2,0,0,0,...]. a(n) = sum_{i=0..n} C(n+10,i+10)*b(i), where b(i)=[1,2,0,0,0,...]. - Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Milan Janjic, Two Enumerative Functions

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n) = 2*C(n+11, 11) - C(n+10, 10). - Paul Barry, Mar 04 2003

a(n) = C(n+10,10) + 2*C(n+10,11). - Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009

MAPLE

A057788 := proc(n)

        1/39916800*(2*n+11) *(n+10) *(n+9) *(n+8) *(n+7) *(n+6) *(n+5) *(n+4) *(n+3) *(n+2) *(n+ 1) ; end proc: # R. J. Mathar, Mar 22 2011

MATHEMATICA

s1=s2=s3=s4=s5=s6=s7=s8=s9=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; s8+=s7; s9+=s8; AppendTo[lst, s9], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 15 2009 *)

PROG

(PARI) Vec((1+x)/(1-x)^12+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Cf. A054334, A054333, A053347, A002415, A005585, A040977, A050486.

Partial sums of A054334.

Sixth column of A111125 (s=5, without leading zeros). - Wolfdieter Lang, Oct 18 2012

Sequence in context: A161465 A162300 A161859 * A166215 A131700 A156947

Adjacent sequences:  A057785 A057786 A057787 * A057789 A057790 A057791

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 04 2000

STATUS

approved

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Last modified August 30 22:25 EDT 2015. Contains 261220 sequences.