OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..447
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(0) = 1; a(n) = Sum_{m=1..n} Sum_{k=m..n} k!*binomial(m,k-m)*stirling1(n,k)/m! for n>0.
a(n) = Sum_{k=0..n} A047974(k) * Stirling1(n,k). - Seiichi Manyama, May 14 2022
PROG
(Maxima)
a(n):=sum(sum(k!*binomial(m, k-m)*stirling1(n, k), k, m, n)/m!, m, 1, n);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)*(1+log(1+x))))) \\ Seiichi Manyama, May 14 2022
(PARI) a(n) = sum(k=0, n, k!*sum(j=0, k\2, 1/(j!*(k-2*j)!))*stirling(n, k, 1)); \\ Seiichi Manyama, May 14 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Apr 21 2011
STATUS
approved