OFFSET
0,3
FORMULA
a(n) = n!*sum(k=1..n, sum(j=0..k, k!*sum(m=floor((k-j)/2)..(n-j)/2, (stirling2(n-2*m,j)*stirling2(m,k-j))/((n-2*m)!*(m!))))), n>0, a(0)=1.
a(n) ~ n!/((exp(r)+2*exp(r^2)*r)*r^(n+1)), where r = 0.522452131... is the root of the equation exp(r)+exp(r^2) = 3. - Vaclav Kotesovec, Jun 27 2013
MATHEMATICA
CoefficientList[Series[1/(3-Exp[x]-Exp[x^2]), {x, 0, 30}], x] Range[0, 30]! (* Harvey P. Dale, Aug 15 2011 *)
PROG
(Maxima)
a(n):=n!*if n=0 then 0 else sum(sum(k!*sum((stirling2(n-2*m, j)*stirling2(m, k-j))/((n-2*m)!*(m!)), m, floor((k-j)/2), (n-j)/2), j, 0, k), k, 1, n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Aug 10 2011
STATUS
approved