A308490 a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(2*k).

1, 1, 17, 778, 70023, 10439451, 2327592658, 725325847443, 301054612941037, 160546901676583432, 106969402879501806589, 87079496403914056543799, 85043317211453886535179728, 98135961356804028347727824541, 132097548629285541942722646521053

Offset: 0

Author

Vaclav Kotesovec, May 31 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..214

Crossrefs

Cf. A229261, A282190, A308491, A316747, A323280, A351182.

Programs

Mathematica

Join[{1}, Table[Sum[k^(2*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 20}]]

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*(exp(x)-1))^k/k!))) \\ Seiichi Manyama, Feb 04 2022

Formula

a(n) ~ exp(exp(-2)/2) * n^(2*n).

E.g.f.: Sum_{k>=0} (k^2 * (exp(x) - 1))^k / k!. - Seiichi Manyama, Feb 04 2022