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 1-4 of 4 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

A368271 Expansion of e.g.f. exp(2*x) / (1 + x*exp(x)).

Original entry on oeis.org

1, 1, 0, -1, 4, 7, -74, 23, 2136, -7345, -77006, 712879, 2499124, -69799897, 88342398, 7311735143, -50617554896, -762825930977, 12821702643946, 56041362405119, -2956159258069044, 8447845572175031, 660257137187089270, -7376306690095890185
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A302397, A368272, A368273.
Cf. A368265, A368267.

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!.

A368268 Expansion of e.g.f. exp(-x) / (1 - 2*x*exp(x)).

Original entry on oeis.org

1, 1, 9, 71, 817, 11599, 197881, 3938087, 89569761, 2291869727, 65159228521, 2037767466679, 69521938950289, 2569515452879855, 102274007835523161, 4361566914028222919, 198403133940750790081, 9589223805173365594687, 490729273233730201604809
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A351762, A368236, A368267, A368269.

Programs

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

Formula

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

A368269 Expansion of e.g.f. exp(-2*x) / (1 - 2*x*exp(x)).

Original entry on oeis.org

1, 0, 8, 46, 584, 8138, 139252, 2770206, 63009648, 1612255186, 45837395564, 1433503025414, 48906419204392, 1807570412699322, 71946432680652324, 3068220235065662062, 139570141248903198944, 6745706553985526731682, 345212056986241161670876
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A351762, A368236, A368267, A368268.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k-2)^k / k!.
Showing 1-4 of 4 results.

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

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