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%I #4 Oct 16 2016 14:49:53
%S 1,3,41,1531,111393,13262051,2336744233,570621092091,184341785557121,
%T 76092709735150723,39064090158380196201,24408768326642565035963,
%U 18237590837527919131499041,16056004231253610384348995811,16448689708899063469247204152553
%N a(n) = Sum_{k=0..n} binomial(n,k) * 2^k * n^k * k!.
%F a(n) = exp(1/(2*n)) * 2^n * n^n * Gamma(n+1, 1/(2*n)).
%F a(n) ~ 2^n * n^n * n!.
%t Flatten[{1, Table[Sum[Binomial[n, k]*2^k*n^k*k!, {k, 0, n}], {n, 1, 20}]}]
%Y Cf. A086331, A277373, A277423, A277452.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Oct 16 2016