A357093 E.g.f. satisfies A(x)^A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2).

1, 0, 0, 6, 36, 210, 3150, 55104, 890232, 16735944, 386223120, 9790441056, 265867900056, 7943197796352, 260063260578576, 9156071916788544, 344740627648393920, 13880862578534022720, 595178180505073088640, 27035591386823290224000

Offset: 0

Author

Seiichi Manyama, Sep 11 2022

Keywords

• nonn

Crossrefs

Cf. A141209, A357092.

Cf. A357029.

Programs

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 A(x) * log(A(x)) = -log(1 - x * A(x))^3.

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * |Stirling1(n,3*k)|/k!.