A384471 a(n) = Sum_{k=0..n} binomial(n,k)^2 * Stirling2(2*k,k) * Stirling2(2*n-2*k,n-k).

1, 2, 18, 306, 8046, 296100, 14307254, 865996306, 63308257198, 5432272670376, 535074966419260, 59461066810476232, 7354069129792197762, 1001371912804041913056, 148806933109572134044158, 23958722845801073318076450, 4154065510530807075869275150, 771608888261061026185781127184

Offset: 0

Author

Vaclav Kotesovec, May 30 2025

Keywords

• nonn

Crossrefs

Cf. A187655, A187657, A384470, A384472.

Cf. A226775.

Programs

Mathematica

Table[Sum[StirlingS2[2*k, k]*StirlingS2[2*n-2*k, n-k]*Binomial[n, k]^2, {k, 0, n}], {n, 0, 20}]

Formula

a(n) ~ 2^(3*n + 1/2) * n^(n - 3/2) / (Pi^(3/2) * (1-w) * exp(n) * (2-w)^n * w^n), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599...