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.

A362393 E.g.f. satisfies A(x) = exp(x + x^4 * A(x)).

Original entry on oeis.org

1, 1, 1, 1, 25, 241, 1441, 6721, 87361, 1729729, 24816961, 270452161, 3705324481, 85344916801, 1992230175937, 38047293910081, 709217112938881, 17385498239168641, 514103858592923521, 14254662916125735553, 366807994235438359681, 10338786602768939575681
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2023

Keywords

Links

Crossrefs

Cf. A125500, A362392.
Cf. A362431.

Programs

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

Formula

E.g.f.: exp(x - LambertW(-x^4 * exp(x))) = -LambertW(-x^4 * exp(x))/x^4.
a(n) = n! * Sum_{k=0..floor(n/4)} (k+1)^(n-3*k-1) / (k! * (n-4*k)!).

A362430 E.g.f. satisfies A(x) = exp(x - x^3 * A(x)).

Original entry on oeis.org

1, 1, 1, -5, -47, -239, 121, 19321, 261409, 1449505, -20428559, -730564559, -10403326559, -10910781023, 3713153976169, 108037345645321, 1301173754543041, -22441761904964159, -1628466860540690207, -41339196023230498463, -189173461196772118079
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2023

Keywords

Links

Crossrefs

Cf. A362396, A362431.
Cf. A362392.

Programs

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

Formula

E.g.f.: exp(x - LambertW(x^3 * exp(x))) = LambertW(x^3 * exp(x))/x^3.
a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * (k+1)^(n-2*k-1) / (k! * (n-3*k)!).

A362396 E.g.f. satisfies A(x) = exp(x - x^2 * A(x)).

Original entry on oeis.org

1, 1, -1, -11, -11, 381, 2461, -21083, -449623, 221113, 99327961, 862237641, -24117649907, -612442461227, 3958786971413, 388794711373741, 2915530533136081, -239559177608638095, -6208842113295032015, 118603625804273873809, 8571701737898867135861
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2023

Keywords

Links

Crossrefs

Column k=2 of A362394.
Cf. A362430, A362431.
Cf. A125500.

Programs

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

Formula

E.g.f.: exp(x - LambertW(x^2 * exp(x))) = LambertW(x^2 * exp(x))/x^2.
a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).

A362482 E.g.f. satisfies A(x) = exp(x - x^4 * A(x)^4).

Original entry on oeis.org

1, 1, 1, 1, -23, -599, -8999, -104999, -868559, 5246641, 582598801, 21205760401, 571129277401, 11475082596121, 81837031796521, -7904119577117399, -596529385424263199, -28051840646006771999, -991870986521074646879, -21837506791918601443679
Offset: 0

Views

Author

Seiichi Manyama, Apr 21 2023

Keywords

Links

Crossrefs

Cf. A362480, A362481.
Cf. A362431, A362473.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(4*x^4*exp(4*x))/4)))

Formula

E.g.f.: exp(x - LambertW(4*x^4 * exp(4*x))/4) = ( LambertW(4*x^4 * exp(4*x))/(4*x^4) )^(1/4).
a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).
Showing 1-4 of 4 results.

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