A184947 Expansion of e.g.f. exp(x)*(1-x)^(-x).

1, 1, 3, 10, 45, 241, 1525, 11096, 91441, 842185, 8577871, 95768454, 1163339221, 15278140593, 215739927481, 3259925357716, 52489756856993, 897249441166993, 16228613753092315, 309660835748163394, 6216734677256575581, 130994769191324727697

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2011-2013.

Formula

E.g.f.: exp(x)*(1-x)^(-x).

a(n) = sum(k=0..n, C(n,k) *sum(j=0..k, C(k,j) *abs(Stirling1(n-k,j)) *j!)).

a(n) ~ n! * exp(1). - Vaclav Kotesovec, Aug 13 2013

Maple

with(combinat):
a:= n-> add(binomial(n, k) *add(binomial(k, j)
             *abs(stirling1(n-k, j)) *j!, j=0..k), k=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 03 2011

Mathematica

With[{nn=25}, CoefficientList[Series[Exp[x](1-x)^-x, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 26 2011 *)

Crossrefs

Sequence in context: A355719 A028417 A060311 * A330250 A207652 A099237

Adjacent sequences: A184944 A184945 A184946 * A184948 A184949 A184950

Keyword

nonn

Author

Vladimir Kruchinin, Feb 02 2011

Status

approved