A336180 a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k)^3.

1, 0, -11, 136, -639, -25624, 1133245, -27431424, 259448833, 17402599792, -1405909697499, 63884679938960, -1830503703899519, -5324845289379264, 5494299851213052685, -496909924804074650624, 30201149245542631276545, -1236819213672144144878752, 5410434345252588202534741

Offset: 0

Author

Seiichi Manyama, Jul 10 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..375
• Vaclav Kotesovec, Plot of |a(n)/a(n-1)|/n for n = 1..1000

Crossrefs

Main diagonal of A336179.

Cf. A241247, A307885.

Programs

Maple

a := n -> hypergeom([-n, -n, -n], [1, 1], n):
seq(simplify(a(n)), n=0..18); # Peter Luschny, Dec 22 2020

Mathematica

Array[Function[n, 1 + Sum[(-n)^k Binomial[n, k]^3, {k, n}]], 19, 0] (* Jan Mangaldan, Jul 14 2020 *)

PARI

{a(n) = sum(k=0, n, (-n)^k*binomial(n, k)^3)}

Formula

a(n) = hypergeom([-n, -n, -n], [1, 1], n). - Peter Luschny, Dec 22 2020