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 A193939 E.g.f.: A(x) = 1/(3-exp(x)-exp(x^2)). 0
 1, 1, 5, 25, 207, 1901, 22323, 295597, 4554763, 78201805, 1499474883, 31541086853, 724817679171, 18030594344725, 483229053783115, 13872831410796973, 424869901099340235, 13824490678644370109, 476299421571109945971, 17321461645693901532181, 663085324931813890398355 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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 Sequence in context: A346269 A337041 A254335 * A229810 A080631 A080632 Adjacent sequences:  A193936 A193937 A193938 * A193940 A193941 A193942 KEYWORD nonn AUTHOR Vladimir Kruchinin, Aug 10 2011 STATUS approved

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Last modified September 25 19:04 EDT 2021. Contains 347659 sequences. (Running on oeis4.)