A367200 -id:A367200 - cp's OEIS frontend

A367199 E.g.f. satisfies A(x) = (1 + x*A(x))^(A(x)^3).

1, 1, 8, 141, 3852, 143460, 6780642, 388851960, 26235133992, 2036243259648, 178742696099040, 17509589369568648, 1893647907646728120, 224106838102512869400, 28809018473999642686584, 3997516614926297143604760, 595518793080901690966354368

Offset: 0

Seiichi Manyama, Nov 10 2023

nonn

Cf. A349505, A367157.
Cf. A162655, A162656.
Cf. A367200, A367201.

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

a(n) = Sum_{k=0..n} (n+3*k+1)^(k-1) * Stirling1(n,k).

A367201 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1) A(x)^3.

Original entry on oeis.org

1, 1, 10, 200, 6167, 258607, 13748744, 886397829, 67211684890, 5861684458896, 578088714806497, 63617223837958309, 7728596914020856162, 1027393177458209939977, 148344954037140113652010, 23119776330887635387231580, 3868359765874829925197165527

Offset: 0

Seiichi Manyama, Nov 10 2023

nonn

Cf. A349525, A367163.
Cf. A349557, A355762.
Cf. A367199, A367200.

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

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

cp's OEIS Frontend

A367199 E.g.f. satisfies A(x) = (1 + x*A(x))^(A(x)^3).

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A367201 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1) A(x)^3.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A367199 E.g.f. satisfies A(x) = (1 + x*A(x))^(A(x)^3).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A367201 E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^3.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A367201 E.g.f. satisfies log(A(x)) = (exp(xA(x)) - 1) A(x)^3.