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 1-6 of 6 results.

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

A362349 a(n) = n! * Sum_{k=0..floor(n/4)} k^k / (k! * (n-4*k)!).

Original entry on oeis.org

1, 1, 1, 1, 25, 121, 361, 841, 82321, 728785, 3633841, 13313521, 2195435881, 28125394441, 196393341145, 981274727161, 227100486456481, 3807339471993121, 34186011461595361, 216366574074187105, 64438384450412161081, 1335035336388170601241
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A086331, A362347, A362348.

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)).

A362523 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) / (k! * (n-3*k)!).

Original entry on oeis.org

1, 1, 1, 7, 25, 61, 1201, 7771, 30577, 1058905, 9904321, 53722351, 2708688841, 33126146197, 228967340785, 15262865820931, 230517745701601, 1936173471789361, 161021598306402817, 2894434429492525015, 28614958982310290041
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2023

Keywords

Links

Crossrefs

Cf. A088957, A362522.
Cf. A089464, A362348.

Programs

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

Formula

E.g.f.: exp(x - LambertW(-x^3)) = -LambertW(-x^3)/x^3 * exp(x).
a(n) ~ sqrt(3) * (exp(3*exp(-1/3)/2) + 2*cos(sqrt(3)*exp(-1/3)/2 - 2*Pi*n/3)) * n^(n-1) / exp(2*n/3 + exp(-1/3)/2 - 1). - Vaclav Kotesovec, Aug 05 2025

A362338 a(n) = n! * Sum_{k=0..floor(n/3)} (-k)^k / (k! * (n-3*k)!).

Original entry on oeis.org

1, 1, 1, -5, -23, -59, 1321, 9871, 39985, -1512503, -16027919, -89148509, 4751428441, 65256458125, 461686022617, -31737431328329, -535583971806239, -4599769739165039, 387180506424212065, 7750866424109754187, 78298694889496869961, -7798395141074580424619
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A069856, A362337, A362339.
Cf. A362348.

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)).

A362341 a(n) = n! * Sum_{k=0..floor(n/3)} (-k/6)^k / (k! * (n-3*k)!).

Original entry on oeis.org

1, 1, 1, 0, -3, -9, 21, 246, 1065, -4283, -67319, -397484, 2315941, 45914155, 343743037, -2623221054, -62980998639, -571382718039, 5391435590545, 152175023203432, 1622112809355661, -18232162910685569, -591788241447761819, -7247966654986009490
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A069856, A362340, A362342.
Cf. A351929, A362303, A362348.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^3/6))))

Formula

E.g.f.: exp(x) / (1 + LambertW(x^3/6)).

A362703 Expansion of e.g.f. 1/(1 + LambertW(-x^3 * exp(x))).

Original entry on oeis.org

1, 0, 0, 6, 24, 60, 1560, 20370, 161616, 2601144, 53827920, 829605150, 14894289960, 360575394036, 8234733389064, 188800085076330, 5145737430116640, 148419618327231600, 4278452209330445856, 134018446273097264694, 4529883358179857555640
Offset: 0

Views

Author

Seiichi Manyama, Apr 30 2023

Keywords

Links

Crossrefs

Cf. A072034, A362702.
Cf. A292889, A362348, A362699.

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-2*k) / (k! * (n-3*k)!).
Showing 1-6 of 6 results.

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

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