A368292 -id:A368292 - cp's OEIS frontend

A368293 Expansion of e.g.f. exp(2x) / (1 - xexp(3*x)).

1, 3, 16, 137, 1572, 22457, 384934, 7699449, 176004376, 4526214641, 129331581954, 4065059876033, 139385578253524, 5177627842411065, 207123084913936174, 8877473910719477033, 405862594146337680816, 19715036609777115714401, 1014004150296746677804666

Offset: 0

Seiichi Manyama, Dec 19 2023

Cf. A336948, A368292.

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

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

A368291 Expansion of e.g.f. exp(x) / (1 - xexp(2x)).

Original entry on oeis.org

1, 2, 9, 64, 601, 7046, 99169, 1628404, 30558609, 645145642, 15133509721, 390493864520, 10992015298345, 335198866337518, 11008101913855089, 387333950619801916, 14537422513124682913, 579719887191660443858, 24477810534426983873833

Offset: 0

Seiichi Manyama, Dec 19 2023

Cf. A368292.

With[{nn=20},CoefficientList[Series[Exp[x]/(1-x Exp[2x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 27 2025 *)

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

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

cp's OEIS Frontend

A368293 Expansion of e.g.f. exp(2x) / (1 - xexp(3*x)).

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A368291 Expansion of e.g.f. exp(x) / (1 - xexp(2x)).

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Author

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PARI

Formula

cp's OEIS Frontend

A368293 Expansion of e.g.f. exp(2*x) / (1 - x*exp(3*x)).

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Author

Keywords

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Formula

A368291 Expansion of e.g.f. exp(x) / (1 - x*exp(2*x)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Formula

A368293 Expansion of e.g.f. exp(2x) / (1 - xexp(3*x)).

A368291 Expansion of e.g.f. exp(x) / (1 - xexp(2x)).