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 1-5 of 5 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

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)).

A362522 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) / (k! * (n-2*k)!).

Original entry on oeis.org

1, 1, 3, 7, 49, 201, 2491, 14743, 266337, 2055889, 49051891, 466650471, 13873711633, 156839920537, 5591748678699, 73222243463671, 3046762637864641, 45346835284775073, 2158148557098011107, 35980450963558606279, 1928292118820446611441
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2023

Keywords

Links

Crossrefs

Cf. A088957, A362523.
Cf. A089461, A362347.

Programs

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

Formula

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

A362702 Expansion of e.g.f. 1/(1 + LambertW(-x^2 * exp(x))).

Original entry on oeis.org

1, 0, 2, 6, 60, 500, 6150, 81522, 1300376, 23024808, 459915210, 10104914270, 243652575012, 6378414900156, 180405368976014, 5478759958122570, 177868544365861680, 6146407749811022672, 225262698504062963346, 8727083181657584963766
Offset: 0

Views

Author

Seiichi Manyama, Apr 30 2023

Keywords

Links

Crossrefs

Cf. A072034, A362703.
Cf. A216507, A362347.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2*exp(x)))))

Formula

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

A362337 a(n) = n! * Sum_{k=0..floor(n/2)} (-k)^k / (k! * (n-2*k)!).

Original entry on oeis.org

1, 1, -1, -5, 37, 221, -2549, -21041, 342665, 3604537, -75816809, -970017949, 25012223149, 377031935125, -11513789879773, -199833956857289, 7052339905578001, 138505710577529969, -5546345926322582225, -121599560980889072693, 5447342134797972438581
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2023

Keywords

Links

Crossrefs

Cf. A069856, A362338, A362339.
Cf. A362347.

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)).
Showing 1-5 of 5 results.

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

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