A356892
E.g.f. satisfies log(A(x)) = x^3 * (exp(x * A(x)) - 1) * A(x).
Original entry on oeis.org
1, 0, 0, 0, 24, 60, 120, 210, 101136, 1089144, 7409520, 39917790, 4097460840, 100410712116, 1474154203704, 16356956618730, 786764261166240, 30867868254267120, 778327514455987296, 14658714575197061814, 522720977799308061240, 25075479032600008569900
Offset: 0
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m = 22; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[x^3*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m-1]! (* Jean-François Alcover, Sep 12 2022 *)
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a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!);
A371023
E.g.f. satisfies log(A(x)) = x*A(x)^2 * (exp(x*A(x)^2) - 1).
Original entry on oeis.org
1, 0, 2, 3, 112, 665, 23016, 292957, 10710960, 223877313, 9010822600, 266949248621, 12012620436312, 461111201730049, 23286625765980864, 1093225826724243045, 61822510319788946656, 3415325919719802626177, 215162865022831595415576
Offset: 0
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a(n) = n!*sum(k=0, n\2, (2*n+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);
A376351
E.g.f. satisfies A(x) = exp( x*A(x)*(exp(x^2*A(x)^2) - 1) ).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 2520, 840, 181440, 6063120, 11642400, 1437337440, 44626982400, 254278664640, 24575197046400, 756010400745600, 9284429893939200, 784770965801222400, 25067890370095372800, 541810656586725926400, 42351473267452597248000, 1461224653966598493772800, 48020130717168717960652800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(x*(1-exp(x^2))))/x))
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a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*stirling(k, n-2*k, 2)/k!);