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%I #5 Jan 22 2021 22:38:27
%S 1,3,43,1211,54812,3572775,313493737,35368945463,4962511954307,
%T 844198388785291,170675800745636572,40352181663578992883,
%U 11008690527354504977193,3426969405868832970281647,1205708016597226199323015459,475502109963529414669658708847
%N a(n) = exp(-1) * Sum_{k>=0} (k*(k + n))^n / k!.
%F a(n) = Sum_{k=0..n} binomial(n,k) * Bell(2*n-k) * n^k.
%t Table[Exp[-1] Sum[(k (k + n))^n/k!, {k, 0, Infinity}], {n, 0, 15}]
%t Join[{1}, Table[Sum[Binomial[n, k] BellB[2 n - k] n^k, {k, 0, n}], {n, 1, 15}]]
%Y Cf. A000110, A020557, A094577, A134980, A334242, A340823.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jan 22 2021
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