OFFSET
0,3
COMMENTS
Exponential transform of A002104. - Seiichi Manyama, May 03 2022
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..448
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
MATHEMATICA
CoefficientList[Series[(1/(1-x))^Exp[x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 21 2013 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 31 2011
STATUS
approved