A320258 a(n) = n! * [x^n] exp(x*exp(-n*x)).

1, 1, -3, 10, 81, -4724, 156205, -4406814, 76958273, 3775676248, -698309272899, 72802616429830, -6310377003297455, 435451735391849892, -10028808876450831571, -4757293711381352201774, 1464955115044140633346305, -310063138309576689774123728, 55179706013436631385620675837

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = [x^n] Sum_{k>=0} x^k/(1 + n*k*x)^(k+1).

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

Mathematica

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

Crossrefs

Cf. A003725, A295552.

Sequence in context: A236696 A262259 A203492 * A136554 A359970 A341848

Adjacent sequences: A320255 A320256 A320257 * A320259 A320260 A320261

Keyword

sign

Author

Ilya Gutkovskiy, Oct 08 2018

Status

approved