A346184 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k^2, n).

1, 1, 6, 96, 2330, 76230, 3132192, 154830704, 8942749020, 590880389676, 43950871549640, 3634094909879808, 330648849617038680, 32827596801363717080, 3531510395923598074560, 409199784951469138012800, 50807611780916913209679632, 6729703201077108496483268880

Offset: 0

Author

Vaclav Kotesovec, Jul 09 2021

Keywords

• nonn

Crossrefs

Cf. A003235, A346183.

Programs

Mathematica

Table[Sum[Binomial[n, k]*Binomial[k^2, n], {k, 0, n}], {n, 0, 20}]

Formula

a(n) ~ 2^(2*n - 1/2) * n^(n - 1/2) / (sqrt(Pi*(1+c)) * exp(n + (2+c)^2/8) * (c*(2+c))^n), where c = LambertW(2*exp(-2)) = 0.21771510575709011079475830443...