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A055251 Eighth column of triangle A055249. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)