OFFSET
0,3
FORMULA
a(n) = sum(m=1..n, (sum(k=0..n-m, (n+k-1)!*sum(j=0..k, 1/(k-j)!*sum(l=0..j, (2^(j-l)*(-1)^(l+j)*stirling1(n-m-l+j,j-l))/(l!*(n-m-l+j)!)))))/(m-1)!), n>0, a(0)=1.
E.g.f.: 4*LambertW(-exp((x-1)/2)/2)^2 / exp(x). - Vaclav Kotesovec, Aug 04 2014
a(n) ~ sqrt(2) * n^(n-1) / (exp(n-1) * (2*log(2)-1)^(n-1/2)). - Vaclav Kotesovec, Aug 04 2014
MATHEMATICA
CoefficientList[Series[4*ProductLog[-E^((x-1)/2)/2]^2/E^x, {x, 0, 15}], x]*Range[0, 15]! (* Vaclav Kotesovec, Aug 04 2014 *)
PROG
(Maxima)
a(n):=(sum((m*sum((n+k-1)!*sum(1/(k-j)!*sum((2^(j-l)*(-1)^(l+j)*stirling1(n-m-l+j, j-l))/(l!*(n-m-l+j)!), l, 0, j), j, 0, k), k, 0, n-m))/m!, m, 1, n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Sep 26 2012
STATUS
approved