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 1-3 of 3 results.

A376476 E.g.f. satisfies A(x) = exp( x^2*A(x)^2 * (1 + x*A(x)) ).

Original entry on oeis.org

1, 0, 2, 6, 60, 720, 8400, 161280, 2857680, 66528000, 1650227040, 45984153600, 1430926136640, 47843446210560, 1760106348000000, 69273962466508800, 2936107841835168000, 132818888849994547200, 6387603066932383296000, 325931634111283200000000, 17558641895241269299276800
Offset: 0

Views

Author

Seiichi Manyama, Sep 24 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*binomial(k, n-2*k)/k!);

Formula

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

A376493 E.g.f. satisfies A(x) = exp(x^3 * (1 + x) * A(x)^3).

Original entry on oeis.org

1, 0, 0, 6, 24, 0, 2520, 35280, 141120, 6048000, 181440000, 1995840000, 51831964800, 2280127449600, 47882676441600, 1192991325926400, 59048471978496000, 1942527607308288000, 56983429057076121600, 2842216483159788134400, 126830901998902413312000
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x^3*(1+x))/3)))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(k, n-3*k)/k!);

Formula

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

A376565 E.g.f. satisfies A(x) = exp( x*A(x) * (1 + x^3*A(x)^3) ).

Original entry on oeis.org

1, 1, 3, 16, 149, 2016, 34447, 692224, 15986889, 420544000, 12494098331, 414681513984, 15201740343517, 609446038061056, 26511336043734375, 1243650774790045696, 62591481040666342673, 3364694927903114919936, 192423068815578523022899, 11665229364232192000000000
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\4, (n+1)^(n-3*k-1)*binomial(n-3*k, k)/(n-3*k)!);

Formula

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