A287700 a(n) = (4!)^3 * [z^4] hypergeom([], [1,1], z)^n.

0, 1, 346, 6219, 36628, 124405, 316206, 672511, 1267624, 2189673, 3540610, 5436211, 8006076, 11393629, 15756118, 21264615, 28104016, 36473041, 46584234, 58663963, 72952420, 89703621, 109185406, 131679439, 157481208, 186900025, 220259026, 257895171, 300159244

Offset: 0

Author

Peter Luschny, May 31 2017

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Column 4 of A287698.

Programs

Magma

[-1899*n + 3916*n^2 - 2592*n^3 + 576*n^4: n in [0..30]]; // Vincenzo Librandi, Jul 20 2017

Maple

a := n -> -1899*n + 3916*n^2 - 2592*n^3 + 576*n^4: seq(a(n), n=0..27);

Mathematica

Table[-1899 n + 3916 n^2 - 2592 n^3 + 576 n^4, {n, 0, 30}] (* Bruno Berselli, Jun 06 2017 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 346, 6219, 36628}, 30] (* Vincenzo Librandi, Jul 20 2017 *)

Formula

O.g.f.: x*(1 + 341*x + 4499*x^2 + 8983*x^3)/(1 - x)^5.

a(n) = -1899*n + 3916*n^2 - 2592*n^3 + 576*n^4.

a(n) = [x^n] (x + 341*x^2 + 4499*x^3 + 8983*x^4) / (1 - x)^5.