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.

A380014 Expansion of e.g.f. 1/sqrt(exp(-2*x) - 2*x).

Original entry on oeis.org

1, 2, 10, 88, 1084, 17176, 332824, 7623904, 201540112, 6038820640, 202246657696, 7486877795200, 303561658686400, 13378863292503424, 636833910410881408, 32559375816074384896, 1779494669204225605888, 103532173699456380625408, 6388705590982575700625920
Offset: 0

Views

Author

Seiichi Manyama, Jan 09 2025

Keywords

Crossrefs

Cf. A072597, A380016, A380018.

Programs

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

Formula

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

A380016 Expansion of e.g.f. 1/(exp(-3*x) - 3*x)^(1/3).

Original entry on oeis.org

1, 2, 13, 161, 2833, 64841, 1827685, 61192181, 2372620801, 104549934977, 5160225776101, 281994042839477, 16902276273364465, 1102519010117525105, 77749077431938305541, 5894145002422856684501, 478015727336387513545345, 41295912476641866286397825, 3786025873450493919700627525
Offset: 0

Views

Author

Seiichi Manyama, Jan 09 2025

Keywords

Crossrefs

Cf. A072597, A380014, A380018.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (-3)^k * (3*k+1)^(n-k) * binomial(-1/3,k)/(n-k)!.

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.

Content is available under The OEIS End-User License Agreement.