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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A055249, A035039, partial sums of A055250.

Sequence in context: A061005 A006550 A047780 * A038733 A004142 A006529

Adjacent sequences: A055248 A055249 A055250 * A055252 A055253 A055254

Keyword

easy,nonn

Author

Wolfdieter Lang, May 26 2000

Status

approved