A057658 a(n) = n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4).

0, 8640, 172800, 1512000, 8467200, 35562240, 121927680, 359251200, 940896000, 2242468800, 4947022080, 10231341120, 20033395200, 37425024000, 67118284800, 116138603520, 194702952960, 317346724800, 504348768000, 783510235200

Offset: 0

Author

N. J. A. Sloane, Oct 16 2000

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).

Crossrefs

Cf. A047819.

Programs

Magma

[n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4): n in [0..25]]; // Vincenzo Librandi, Jun 07 2019

Maple

seq(n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4), n=0..30); # Robert Israel, Jun 06 2019

Mathematica

Table[n (n+1)^2 (n+2)^3 (n+3)^2 (n+4), {n, 0, 40}] (* Vincenzo Librandi, Jun 07 2019 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0,8640,172800,1512000,8467200,35562240,121927680,359251200,940896000,2242468800},30] (* Harvey P. Dale, Sep 24 2021 *)

Formula

From Robert Israel, Jun 06 2019: (Start)

G.f.: 8640*x*(x^4 + 10*x^3 + 20*x^2 + 10*x + 1)/(x - 1)^10.

(n + 3)*(n + 2)*a(n - 2) - 2*(n^2 + 2*n + 12)*a(n - 1) + n*(n - 1)*a(n) = 0. (End)

a(n) = 8640*A047819(n) for n > 0. - Michel Marcus, Jun 07 2019