A323533 a(n) = Product_{k=1..n} (binomial(k-1,5) + binomial(n-k,5)).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 790420571136, 100389735898841088, 14582663231533605863424, 2458550581659926554038239232, 529554691027323329170207744475136, 146980847512952623091566575072055001088, 53003014923687519392206631372837133989462016

Offset

0,11

Links

Robert Israel, Table of n, a(n) for n = 0..128

Formula

a(n) ~ exp((1 + 2*Pi*sqrt(5 - 2/sqrt(5))/5) * (n-5)) * n^(5*n) / (exp(5*n)*120^n).

Maple

f:= proc(n) local k;
mul(binomial(k-1, 5) + binomial(n-k, 5), k=1..n)
end proc:
map(f, [$0..25]); # Robert Israel, Jun 03 2026

Mathematica

Table[Product[Binomial[k-1, 5] + Binomial[n-k, 5], {k, 1, n}], {n, 0, 20}]

Prog

(PARI) a(n) = prod(k=1, n, binomial(k-1, 5) + binomial(n-k, 5)); \\ Michel Marcus, Jan 17 2019

Crossrefs

Cf. A000389, A323425, A323496, A323497, A323534, A323535.

Sequence in context: A384745 A233806 A066543 * A233800 A162027 A172616

Adjacent sequences: A323530 A323531 A323532 * A323534 A323535 A323536

Keyword

nonn,changed

Author

Vaclav Kotesovec, Jan 17 2019

Status

approved