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A057788 Expansion of (1+x)/(1-x)^12. 11
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

2*a(n) is number of ways to place 10 queens on an (n+10) X (n+10) chessboard so that they diagonally attack each other exactly 45 times. The maximal possible attack number, p=binomial(k,2) =45 for k=10 queens, is achievable only when all queens are on the same diagonal. In graph-theory representation they thus form the corresponding complete graph. - Antal Pinter, Dec 27 2015

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.

Index entries for linear recurrences with constant coefficients, signature (12,-66, 220,-495,792,-924,792,-495,220,-66,12,-1).

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

a(n) = C(n+10,10)*(2n+11)/11. - Antal Pinter, Dec 27 2015

a(n) = 12*a(n-1)-66*a(n-2)+220*a(n-3)-495*a(n-4)+792*a(n-5)-924*a(n-6)+792*a(n-7)-495*a(n-8)+220*a(n-9)-66*a(n-10)+12*a(n-11)-a(n-12) for n >11. - Vincenzo Librandi, Feb 14 2016

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 *)

CoefficientList[Series[(1 + x) / (1 - x)^12, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 14 2016 *)

PROG

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

(MAGMA) [Binomial(n+10, 10)*(2*n+11)/11: n in [0..40]]; // Vincenzo Librandi, Feb 14 2016

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 * A267175 A266767 A166215

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 May 5 23:38 EDT 2016. Contains 272475 sequences.