A371230 E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^2).
1, 0, 2, 3, 128, 750, 29964, 377160, 15795072, 329631120, 15001287120, 449174341440, 22551082739712, 885381886509120, 49302509206648320, 2391802812599316480, 147728974730632012800, 8502972330919072688640, 580806950108814502345728
Offset: 0
Programs
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Mathematica
terms=19; A[]=1; Do[A[x]= 1 - x*A[x]^3*Log[1 - x*A[x]^2] + O[x]^terms//Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]*Range[0,terms-1]! (* Stefano Spezia, Sep 03 2025 *)
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PARI
a(n) = n!*sum(k=0, n\2, (2*n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(2*n+1)!;
Formula
a(n) = (n!/(2*n+1)!) * Sum_{k=0..floor(n/2)} (2*n+k)! * |Stirling1(n-k,k)|/(n-k)!.