A057666 a(n) = n*(n+1)^2*(n+2)*(n+3)^2*(n+4).

0, 960, 10800, 60480, 235200, 725760, 1905120, 4435200, 9408960, 18532800, 34354320, 60540480, 102211200, 166333440, 262180800, 401863680, 600935040, 879076800, 1260871920, 1776667200, 2463531840, 3366316800, 4538820000, 6045062400, 7960680000, 10374436800, 13389863760

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

From Amiram Eldar, Jun 16 2026: (Start)

G.f.: 240 * x * (4*x^2 + 13*x + 4)/(x-1)^8.

E.g.f.: exp(x) * x * (x^6 + 35*x^5 + 428*x^4 + 2260*x^3 + 5160*x^2 + 4440*x + 960).

Sum_{n>=1} 1/a(n) = 1/864.

Sum_{n>=1} (-1)^(n+1)/a(n) = 89/288 - 4*log(2)/9. (End)

Mathematica

a[n_] := n*(n+1)^2*(n+2)*(n+3)^2*(n+4); Array[a, 27, 0] (* Amiram Eldar, Jun 16 2026 *)

Crossrefs

Sequence in context: A158412 A247723 A330496 * A046788 A206079 A203732

Adjacent sequences: A057663 A057664 A057665 * A057667 A057668 A057669

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 16 2000

Extensions

More terms from Amiram Eldar, Jun 16 2026

Status

approved