%I #13 Feb 18 2022 13:51:01

%S 1,1,15,683,61332,9135004,2035708760,634172615600,263166948202080,

%T 140322186951905736,93484350581344936344,76095870609142447018152,

%U 74311960997497053384537408,85748280952260853814490688656

%N a(n) = Sum_{k=0..n} k^(2*k) * Stirling1(n,k).

%F E.g.f.: Sum_{k>=0} (k^2 * log(1+x))^k / k!.

%F a(n) ~ exp(-exp(-2)/2) * n^(2*n). - _Vaclav Kotesovec_, Feb 18 2022

%o (PARI) a(n) = sum(k=0, n, k^(2*k)*stirling(n, k, 1));

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*log(1+x))^k/k!)))

%Y Cf. A308490, A305819, A350721, A351180, A351183.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 04 2022