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.

A362348 a(n) = n! * Sum_{k=0..floor(n/3)} k^k / (k! * (n-3*k)!).

Original entry on oeis.org

1, 1, 1, 7, 25, 61, 1561, 10291, 40657, 1754425, 16632721, 90479071, 5469933481, 67591594357, 468224398825, 36386954606731, 554182030325281, 4663003095358321, 442756825853252257, 8014853488848923575, 79354642490200806841, 8901962495566386752941
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A086331, A362347, A362349.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^3))))

Formula

E.g.f.: exp(x) / (1 + LambertW(-x^3)).
a(n) ~ (exp(3*exp(-1/3)/2) + 2*cos(sqrt(3)*exp(-1/3)/2 - 2*Pi*n/3)) * n^n / (sqrt(3) * exp(2*n/3 + exp(-1/3)/2)). - Vaclav Kotesovec, Apr 18 2023

A362347 a(n) = n! * Sum_{k=0..floor(n/2)} k^k / (k! * (n-2*k)!).

Original entry on oeis.org

1, 1, 3, 7, 61, 261, 3991, 24403, 524217, 4149001, 114544171, 1111976031, 37492210933, 431097055117, 17165526306111, 228085258466731, 10472666396599921, 157882659583461393, 8211536252680154707, 138474928851961700791, 8045878340298511456941
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A086331, A362348, A362349.
Cf. A277614.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2))))

Formula

E.g.f.: exp(x) / (1 + LambertW(-x^2)).
a(n) ~ (exp(2*exp(-1/2)) + (-1)^n) * n^n / (sqrt(2) * exp(n/2 + exp(-1/2))). - Vaclav Kotesovec, Aug 05 2025

A362339 a(n) = n! * Sum_{k=0..floor(n/4)} (-k)^k / (k! * (n-4*k)!).

Original entry on oeis.org

1, 1, 1, 1, -23, -119, -359, -839, 78961, 722737, 3623761, 13297681, -2115602279, -27917827079, -195909017303, -980236890359, 219254440161121, 3780662914771681, 34105981790126881, 216149350680413857, -62275804867272039479, -1325952502191492278039
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A069856, A362337, A362338.
Cf. A362349.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^4))))

Formula

E.g.f.: exp(x) / (1 + LambertW(x^4)).

A362342 a(n) = n! * Sum_{k=0..floor(n/4)} (-k/24)^k / (k! * (n-4*k)!).

Original entry on oeis.org

1, 1, 1, 1, 0, -4, -14, -34, 71, 1135, 6091, 22771, -87119, -1847559, -13769755, -70046339, 390688481, 10473961121, 100030347361, 643972996705, -4717305354419, -153449916040259, -1787926183752939, -13926752488607419, 126329848106764765
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A069856, A362340, A362341.
Cf. A351930, A362345, A362349.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^4/24))))

Formula

E.g.f.: exp(x) / (1 + LambertW(x^4/24)).
Showing 1-4 of 4 results.

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

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