A357088 -id:A357088 - cp's OEIS frontend

A357089 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3 / 6.

1, 0, 0, 1, 6, 25, 140, 1561, 19586, 228425, 2870160, 44172601, 780614846, 14499946825, 284310704860, 6089231941521, 142225796401786, 3537029819020905, 92766573133851240, 2577870903366020521, 75999605064376599606, 2362944241092314079145

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349588, A357088.

a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*stirling(n, 3*k, 2)/(6^k*k!));

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * Stirling2(n,3*k)/(6^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

A357089 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3 / 6.

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