A055251 Eighth column of triangle A055249.

1, 10, 57, 244, 874, 2772, 8054, 21920, 56751, 141326, 341303, 804276, 1858080, 4223784, 9474444, 21018144, 46195149, 100734354, 218190469, 469866964, 1006759110, 2147634364, 4563581746, 9663887808, 20401343003, 42949963286, 90194651043, 188978952404

Offset: 0

Author

Wolfdieter Lang, May 26 2000

Keywords

• easy
• nonn

Comments

A045618 Partial sums of A000337(n+4),n>=0,

A045889 Partial sums of A045618,

A034009 Partial sums of A045889,

(A055250 Seventh column of triangle A055249) Partial sums of A034009,

(A055251 Eighth column of triangle A055249) Partial sums of A055250. - Vladimir Joseph Stephan Orlovsky, Jul 09 2011

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-43,104,-155,146,-85,28,-4).

Crossrefs

Cf. A055249, A035039, partial sums of A055250.

Programs

Maple

a:= n-> (Matrix(8, (i,j)-> if (i=j-1) then 1 elif j=1 then [10,-43,104,-155, 146,-85,28,-4][i] else 0 fi)^(n))[1,1]: seq(a(n), n=0..25); # Alois P. Heinz, Aug 05 2008

Mathematica

Table[Sum[(-1)^(n - k) k (-1)^(n - k) Binomial[n + 6, k + 6], {k, 0, n}], {n, 1, 26}] (* Zerinvary Lajos, Jul 08 2009 *)

PARI

Vec(1 / ((1 - x)^6*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Sep 20 2017

Formula

G.f.: 1 / (((1-2*x)^2)*(1-x)^6).

a(n) = A055249(n+7, 7).

For n >= 1, a(n) = A035039(n+7) + Sum_{j=0..n-1} a(j).

a(n) = Sum_{k=0..n+6} Sum_{i=0..n+6} (i-k) * C(n-k+6,i+4). - Wesley Ivan Hurt, Sep 19 2017

a(n) = (1/120)*(38520 - 75*2^(9+n) + 2*(9637 + 15*2^(8+n))*n + 4285*n^2 + 525*n^3 + 35*n^4 + n^5). - Colin Barker, Sep 20 2017