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.

A362392 E.g.f. satisfies A(x) = exp(x + x^3 * A(x)).

Original entry on oeis.org

1, 1, 1, 7, 49, 241, 2041, 26041, 282913, 3449377, 57170161, 973059121, 16847893921, 343341027745, 7680743819113, 175958943331081, 4375517632543681, 118932887426911681, 3374685950589927649, 100735118425384221025, 3217474234925998764481
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2023

Keywords

Links

Crossrefs

Column k=6 of A362378.
Cf. A118395, A125500, A362393, A362430.

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)} (k+1)^(n-2*k-1) / (k! * (n-3*k)!).

A362431 E.g.f. satisfies A(x) = exp(x - x^4 * A(x)).

Original entry on oeis.org

1, 1, 1, 1, -23, -239, -1439, -6719, 33601, 1536193, 24171841, 268424641, 1144566721, -47515765439, -1727426116415, -36344982098879, -481057514071679, 1197767242412161, 319851095455612801, 12145632936380316289, 293167011107091899521, 3520557699737168603521
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2023

Keywords

Links

Crossrefs

Cf. A362396, A362430.
Cf. A362393.

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)} (-1)^k * (k+1)^(n-3*k-1) / (k! * (n-4*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)!).

A362481 E.g.f. satisfies A(x) = exp(x - x^3 * A(x)^3).

Original entry on oeis.org

1, 1, 1, -5, -95, -959, -5159, 69721, 3113377, 64493857, 654012721, -13761498959, -1013114081759, -32273321679455, -492845589685175, 13357113599586121, 1410278045569310401, 61239473424756703681, 1270682827211021594977, -40402942687262364034463
Offset: 0

Views

Author

Seiichi Manyama, Apr 21 2023

Keywords

Links

Crossrefs

Cf. A362480, A362482.
Cf. A362430, A362472.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(3*x^3*exp(3*x))/3)))

Formula

E.g.f.: exp(x - LambertW(3*x^3 * exp(3*x))/3) = ( LambertW(3*x^3 * exp(3*x))/(3*x^3) )^(1/3).
a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
Showing 1-4 of 4 results.

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