A344564 a(n) = [x^n] -3/(2*x - 1)^5.

3, 30, 180, 840, 3360, 12096, 40320, 126720, 380160, 1098240, 3075072, 8386560, 22364160, 58490880, 150405120, 381026304, 952565760, 2353397760, 5752750080, 13927710720, 33426505728, 79586918400, 188114534400, 441660211200, 1030540492800, 2390853943296

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Formula

a(n) = 2*(n + 4)*a(n - 1) / n for n >= 2.

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

a(n) = n! * [x^n] (2*x^4 + 16*x^3 + 36*x^2 + 24*x + 3)*exp(2*x).

a(n) ~ 2^(n - 3) * n^4.

From Amiram Eldar, Jul 07 2026: (Start)

Sum_{n>=0} 1/a(n) = 20/9 - 8*log(2)/3.

Sum_{n>=0} (-1)^n/a(n) = 72*log(3/2) - 260/9. (End)

Maple

a := n -> 2^(n - 3)*(n + 1)*(n + 2)*(n + 3)*(n + 4): seq(a(n), n = 0..25);

Mathematica

A344564[n_] := 2^(n - 3)*(n + 1)*(n + 2)*(n + 3)*(n + 4);
Array[A344564, 30, 0] (* Paolo Xausa, Jul 02 2026 *)

Crossrefs

Row sums of A344565.

Sequence in context: A127868 A002463 A360645 * A013281 A013274 A013279

Adjacent sequences: A344561 A344562 A344563 * A344565 A344566 A344567

Keyword

nonn,easy

Author

Peter Luschny, May 29 2021

Status

approved