A357084 -id:A357084 - cp's OEIS frontend

A357085 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1)^3 A(x).

1, 0, 0, 6, 36, 150, 3780, 77406, 1059156, 21669990, 640319940, 16622025486, 450085011156, 15416323450710, 561938117029380, 20587443165165246, 835816881563118036, 37282225483118856390, 1722621978491064495300, 83817942806509377794286

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349557, A357084.

Cf. A357025.

a(n) = sum(k=0, n\3, (3*k)!*(n+k+1)^(k-1)*stirling(n, 3*k, 2)/k!);

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+k+1)^(k-1) * Stirling2(n,3*k)/k!.

A357086 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2.

Original entry on oeis.org

1, 0, 2, 6, 50, 510, 5882, 88326, 1502258, 29368590, 650366762, 15974149686, 433095937826, 12829712583870, 412295632858202, 14292175302568806, 531485147656990994, 21107739762958541550, 891673745283286886282, 39923664347178352362006

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349588, A357087.

Cf. A357084, A357088.

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

a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n-k+1)^(k-1) * Stirling2(n,2*k)/k!.

cp's OEIS Frontend

A357085 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1)^3 A(x).

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A357086 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2.

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Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A357085 E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^3 * A(x).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A357086 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A357085 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1)^3 A(x).