A349556 -id:A349556 - cp's OEIS frontend

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

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349556, A357091.

Cf. A357028.

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

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!.

A357091 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 * A(x)).

Original entry on oeis.org

1, 0, 0, 6, 36, 210, 4590, 85344, 1353912, 30525384, 836587440, 22585438656, 676820305656, 23377203675072, 857981143380816, 33416782099297344, 1417453025671696320, 64371985604089220160, 3086958605328618687360, 157142856384519974847360

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349556, A357090.

Cf. A357029.

a(n) = sum(k=0, n\3, (3*k)!*(n+k+1)^(k-1)*abs(stirling(n, 3*k, 1))/k!);

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!.

cp's OEIS Frontend

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

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