A287701 a(n) = (5!)^3 * [z^5] hypergeom([], [1,1], z)^n.

0, 1, 2252, 111753, 1297504, 7120505, 25461756, 70250257, 163191008, 335493009, 629597260, 1100904761, 1819504512, 2871901513, 4362744764, 6416555265, 9179454016, 12820890017, 17535368268, 23544177769, 31097119520, 40474234521, 51987531772, 65982716273, 82840917024, 102980415025, 126858371276, 154972554777

Offset: 0

Author

Peter Luschny, Jun 01 2017

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Column 5 of A287698.

Programs

Maple

a := n -> 163476*n - 375375*n^2 + 305500*n^3 - 108000*n^4 + 14400*n^5:
seq(a(n), n=0..27);

Mathematica

Table[163476 n - 375375 n^2 + 305500 n^3 - 108000 n^4 + 14400 n^5, {n, 0, 30}] (* Bruno Berselli, Jun 06 2017 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,2252,111753,1297504,7120505},30] (* Harvey P. Dale, Mar 02 2025 *)

Formula

O.g.f.: x*(1 + 2246*x + 98256*x^2 + 660746*x^3 + 966751*x^4) / (1 - x)^6.

a(n) = 163476*n - 375375*n^2 + 305500*n^3 - 108000*n^4 + 14400*n^5.

a(n) = [x^n] (x + 2246*x^2 + 98256*x^3 + 660746*x^4 + 966751*x^5) / (1 - x)^6.