A295552 a(n) = n! * [x^n] exp(x*exp(n*x)).

1, 1, 5, 46, 689, 15476, 483157, 19719022, 1009495489, 63119450152, 4728073048901, 417482964953594, 42834647403146161, 5043607239173464924, 674409403861210214485, 101517071981284179924526, 17074451852556909059698433, 3187883879639402167714593488, 656838643288782957496595002117

Offset: 0

Author

Ilya Gutkovskiy, Nov 23 2017

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000248, A216689, A292914.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[x Exp[n x]], {x, 0, n}], {n, 0, 18}]
Join[{1}, Table[Sum[Binomial[n, k] (n k)^(n - k), {k, 0, n}], {n, 1, 18}]]

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*(n*k)^(n-k).