A277453 a(n) = Sum_{k=0..n} binomial(n,k) * 2^k * n^k * k!.

1, 3, 41, 1531, 111393, 13262051, 2336744233, 570621092091, 184341785557121, 76092709735150723, 39064090158380196201, 24408768326642565035963, 18237590837527919131499041, 16056004231253610384348995811, 16448689708899063469247204152553

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2016

Keywords

• nonn

Crossrefs

Cf. A086331, A277373, A277423, A277452.

Programs

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*2^k*n^k*k!, {k, 0, n}], {n, 1, 20}]}]

Formula

a(n) = exp(1/(2*n)) * 2^n * n^n * Gamma(n+1, 1/(2*n)).

a(n) ~ 2^n * n^n * n!.