A371271 E.g.f. satisfies A(x) = 1 + x*A(x)^3 * (exp(x*A(x)^2) - 1).
1, 0, 2, 3, 124, 725, 28146, 352807, 14395256, 298559529, 13269150190, 394087597211, 19361289265044, 752705527798237, 41083484117561354, 1970818974867113295, 119467697774656366576, 6792102349650727753553, 455778318504089893121766
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, (2*n+k)!*stirling(n-k, k, 2)/(n-k)!)/(2*n+1)!;
Formula
a(n) = (n!/(2*n+1)!) * Sum_{k=0..floor(n/2)} (2*n+k)! * Stirling2(n-k,k)/(n-k)!.