A355763 -id:A355763 - cp's OEIS frontend

A355762 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1) A(x)^2.

1, 1, 8, 125, 2987, 96727, 3963841, 196769897, 11480304448, 770031502467, 58386951857583, 4938864464154469, 461111056016847137, 47101341445053180079, 5225323162578044669492, 625646891309723527419137, 80416734865584980392853799, 11044230667889978466327860347

Offset: 0

Seiichi Manyama, Jul 16 2022

nonn

Cf. A030019, A349557.

Cf. A162656, A355763, A355766.

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

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

A356883 E.g.f. satisfies: A(x)^2 * log(A(x)) = x * (exp(x*A(x)) - 1).

Original entry on oeis.org

1, 0, 2, 3, -8, 5, 696, 2527, -40144, -178407, 8337880, 76134971, -1781542344, -24938260763, 691630553264, 14216543752335, -312910463346464, -9343318015483471, 195539694928047144, 8145971436703039363, -142317653823753257560, -8498984155838272275459

Offset: 0

Seiichi Manyama, Sep 02 2022

sign

Cf. A349560, A356785, A356788, A356789, A356882.

Cf. A355763.

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

a(n) = n! * Sum_{k=0..floor(n/2)} (n-3*k+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.

cp's OEIS Frontend

A355762 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1) A(x)^2.

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A356883 E.g.f. satisfies: A(x)^2 * log(A(x)) = x * (exp(x*A(x)) - 1).

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Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A355762 E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^2.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A356883 E.g.f. satisfies: A(x)^2 * log(A(x)) = x * (exp(x*A(x)) - 1).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A355762 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1) A(x)^2.