A377326 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)) - 1)/A(x).
1, 1, 1, 4, 15, 96, 665, 6028, 60907, 725560, 9591549, 142574004, 2323440119, 41519079616, 803667844993, 16797423268252, 376458083887875, 9014414549836296, 229564623594841637, 6197477089425914692, 176767174407208663759, 5312208220728020517136, 167760328500471584529321
Offset: 0
Programs
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Mathematica
terms=23; A[]=1; Do[A[x] = 1 + (Exp[x*A[x]] - 1)/A[x]+ O[x]^terms // Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]Range[0,terms-1]! (* Stefano Spezia, Aug 28 2025 *)
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PARI
a(n) = sum(k=0, (n+1)\2, (n-k)!/(n-2*k+1)!*stirling(n, k, 2));
Formula
a(n) = Sum_{k=0..floor((n+1)/2)} (n-k)!/(n-2*k+1)! * Stirling2(n,k).