cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

1, 3, 12, 65, 460, 4057, 42922, 529769, 7472808, 118586033, 2090936014, 40554647377, 858082563532, 19668880007129, 485528656965762, 12841428220413593, 362276791422785488, 10859170086870710497, 344648459867067117334, 11546148650974694099201
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A006153, A072597, A092148, A368266.
Cf. A368267, A368271.

Programs

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

Formula

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

A368272 Expansion of e.g.f. exp(-x) / (1 + x*exp(x)).

Original entry on oeis.org

1, -2, 3, -1, -11, 19, 151, -799, -2295, 37367, -16469, -2114531, 9695533, 132142451, -1556927553, -6822608311, 234527654161, -360436983569, -35798255259821, 294290464165685, 5217729367883061, -102317187098688661, -517822188623299097, 31412148276241662049
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A302397, A368271, A368273.

Programs

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

Formula

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

A368273 Expansion of e.g.f. exp(-2*x) / (1 + x*exp(x)).

Original entry on oeis.org

1, -3, 8, -17, 20, 23, -50, -1185, 6648, 20143, -372646, 179111, 25378468, -126050121, -1849977930, 23353880527, 109161798512, -3986970251809, 6487865966386, 680166849412311, -5885809282265124, -109572316727641433, 2250978116175344846, 11909910338327490623
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A302397, A368271, A368272.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * (n-k-2)^k / k!.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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