A357090 E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) * A(x)).

1, 0, 2, 6, 106, 1060, 21728, 396648, 10174764, 267855264, 8517836832, 289596897480, 11137252365600, 461124747706896, 20922578332613904, 1018268757357253920, 53372000211252229392, 2981808910524462942720, 177468245487057424475136

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+k+1)^(k-1) * |Stirling1(n,2*k)|/k!.

Prog

(PARI) a(n) = sum(k=0, n\2, (2*k)!*(n+k+1)^(k-1)*abs(stirling(n, 2*k, 1))/k!);

Crossrefs

Cf. A349556, A357091.

Cf. A357028.

Sequence in context: A294906 A284262 A287935 * A181036 A222854 A351780

Adjacent sequences: A357087 A357088 A357089 * A357091 A357092 A357093

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2022

Status

approved