A368266 -id:A368266 - cp's OEIS frontend

A368265 Expansion of e.g.f. exp(2x) / (1 - xexp(x)).

1, 3, 12, 65, 460, 4057, 42922, 529769, 7472808, 118586033, 2090936014, 40554647377, 858082563532, 19668880007129, 485528656965762, 12841428220413593, 362276791422785488, 10859170086870710497, 344648459867067117334, 11546148650974694099201

Offset: 0

Seiichi Manyama, Dec 19 2023

Cf. A006153, A072597, A092148, A368266.

Cf. A368267, A368271.

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

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

a(n) ~ n! / ((1 + LambertW(1)) * LambertW(1)^(n+2)). - Vaclav Kotesovec, Dec 29 2023

A379992 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.

Original entry on oeis.org

1, 1, 7, 41, 349, 3539, 42451, 585605, 9130297, 158692679, 3041499871, 63712004729, 1447946191957, 35479218963083, 932326476195115, 26153289728300909, 779995883104560241, 24644267406802467215, 822278654588440803511, 28891372907012629446881

Offset: 0

Seiichi Manyama, Jan 07 2025

Cf. A358738, A377529, A379933, A379997.

Cf. A368266, A377530, A379994.

With[{nn=20},CoefficientList[Series[Exp[-3x]/(Exp[-x]-x)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 14 2025 *)

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

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

cp's OEIS Frontend

A368265 Expansion of e.g.f. exp(2x) / (1 - xexp(x)).

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A379992 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.

Views

Author

Keywords

Crossrefs

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Mathematica

PARI

Formula

cp's OEIS Frontend

A368265 Expansion of e.g.f. exp(2*x) / (1 - x*exp(x)).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A379992 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Formula

A368265 Expansion of e.g.f. exp(2x) / (1 - xexp(x)).