A357091 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 * A(x)).
1, 0, 0, 6, 36, 210, 4590, 85344, 1353912, 30525384, 836587440, 22585438656, 676820305656, 23377203675072, 857981143380816, 33416782099297344, 1417453025671696320, 64371985604089220160, 3086958605328618687360, 157142856384519974847360
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (3*k)!*(n+k+1)^(k-1)*abs(stirling(n, 3*k, 1))/k!);
Formula
E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3 * A(x).
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+k+1)^(k-1) * |Stirling1(n,3*k)|/k!.