A191365 Expansion of e.g.f. (1/(1-x))^exp(x).

1, 1, 4, 18, 102, 695, 5485, 49077, 490308, 5404569, 65106103, 850535477, 11972432846, 180605413001, 2906109200293, 49678357272247, 898988188301320, 17167497793440977, 344991795682802331, 7277230501449340417, 160765066207998479698

Offset: 0

Author

Vladimir Kruchinin, May 31 2011

Keywords

• nonn

Comments

Exponential transform of A002104. - Seiichi Manyama, May 03 2022

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A002104, A298374.

Programs

Mathematica

CoefficientList[Series[(1/(1-x))^Exp[x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 21 2013 *)

Maxima

a(n):=sum(sum(binomial(n,i)*k^i*(-1)^(n-k-i)*stirling1(n-i,k),i,0,n-k),k,1,n);

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(x))) \\ Seiichi Manyama, May 03 2022

Formula

a(n) = sum(k=1..n, sum(i=0..n-k, binomial(n,i)*k^i*(-1)^(n-k-i)*Stirling1(n-i,k))), n>0, a(0)=1.

a(n) ~ n! * n^(exp(1)-1)/Gamma(exp(1)) * (1-exp(1)*(exp(1)-1)*log(n)/n). - Vaclav Kotesovec, Jun 21 2013

a(0) = 1; a(n) = Sum_{k=1..n} A002104(k) * binomial(n-1,k-1) * a(n-k). - Seiichi Manyama, May 03 2022