A357085 -id:A357085 - cp's OEIS frontend

A357084 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1)^2 A(x).

1, 0, 2, 6, 98, 990, 19082, 347046, 8512226, 220737390, 6776521082, 225532370646, 8413133799314, 339965749171230, 14995100013227882, 711308930246853126, 36278600375671552322, 1974411768891211652430, 114394542828023045764442

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349557, A357085.

Cf. A357024.

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!.

A357087 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3.

Original entry on oeis.org

1, 0, 0, 6, 36, 150, 2340, 47166, 676116, 10602150, 248197860, 6304530606, 154511054676, 4227889233750, 134462460901860, 4519745455581726, 157756124072317716, 5960350758700381830, 243292987180534250340, 10433760831781705395726, 469420864688765414084436

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349588, A357086.

Cf. A357085, A357089.

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!.

cp's OEIS Frontend

A357084 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1)^2 A(x).

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A357087 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A357084 E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^2 * A(x).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A357087 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A357084 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1)^2 A(x).