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.

A380015 Expansion of e.g.f. 1/sqrt(1 - 2*x*exp(x)).

Original entry on oeis.org

1, 1, 5, 36, 361, 4640, 72771, 1347598, 28778849, 696288888, 18823644595, 562350743306, 18397666000209, 654164843763340, 25118967828553067, 1035914449832324070, 45665488606439586241, 2142825945301659242576, 106641225471890568771747, 5610282675990428302440130
Offset: 0

Views

Author

Seiichi Manyama, Jan 09 2025

Keywords

Crossrefs

Cf. A006153, A380017, A380019.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (-2)^k * k^(n-k) * binomial(-1/2,k)/(n-k)!.
a(n) ~ sqrt(2) * n^n / (sqrt(1 + LambertW(1/2)) * exp(n) * LambertW(1/2)^n). - Vaclav Kotesovec, Jan 23 2025

A380017 Expansion of e.g.f. 1/(1 - 3*x*exp(x))^(1/3).

Original entry on oeis.org

1, 1, 6, 55, 716, 12085, 250726, 6172915, 175903400, 5694587209, 206438732810, 8284550317351, 364605758728828, 17461047965591581, 903964982917764782, 50306323769422679995, 2994799872257498255696, 189906103853462927405329, 12779300537432602189228306
Offset: 0

Views

Author

Seiichi Manyama, Jan 09 2025

Keywords

Crossrefs

Cf. A006153, A380015, A380019.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, (-3)^k*k^(n-k)*binomial(-1/3, k)/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..n} (-3)^k * k^(n-k) * binomial(-1/3,k)/(n-k)!.
a(n) ~ sqrt(2*Pi) * n^(n - 1/6) / (Gamma(1/3) * (1 + LambertW(1/3))^(1/3) * exp(n) * LambertW(1/3)^n). - Vaclav Kotesovec, Jan 23 2025

A380022 Expansion of e.g.f. 1/(exp(-4*x) - 4*x*exp(-3*x))^(1/4).

Original entry on oeis.org

1, 2, 10, 103, 1608, 33201, 850108, 25961489, 920672000, 37177954705, 1684020384036, 84552655333785, 4660526554922032, 279769833061460249, 18167873577214204964, 1268970734106516345721, 94861592588266224161664, 7556876103775629510620193, 639078655735155260051464132
Offset: 0

Views

Author

Seiichi Manyama, Jan 09 2025

Keywords

Crossrefs

Cf. A380018, A380019.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, (-4)^k*(k+1)^(n-k)*binomial(-1/4, k)/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..n} (-4)^k * (k+1)^(n-k) * binomial(-1/4,k)/(n-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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