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%I #22 Feb 18 2022 13:52:26
%S 1,1,17,778,70023,10439451,2327592658,725325847443,301054612941037,
%T 160546901676583432,106969402879501806589,87079496403914056543799,
%U 85043317211453886535179728,98135961356804028347727824541,132097548629285541942722646521053
%N a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(2*k).
%H Seiichi Manyama, <a href="/A308490/b308490.txt">Table of n, a(n) for n = 0..214</a>
%F a(n) ~ exp(exp(-2)/2) * n^(2*n).
%F E.g.f.: Sum_{k>=0} (k^2 * (exp(x) - 1))^k / k!. - _Seiichi Manyama_, Feb 04 2022
%t Join[{1}, Table[Sum[k^(2*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 20}]]
%o (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
%Y Cf. A229261, A282190, A308491, A316747, A323280, A351182.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 31 2019
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