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.

A380879 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x*exp(x)) ).

Original entry on oeis.org

1, 2, 16, 230, 4888, 138442, 4916140, 210270734, 10530743632, 604747157138, 39185881490644, 2828691317839510, 225137088955561144, 19588316964130880474, 1849745928662841982588, 188421660506420000503838, 20594905554562935801454240, 2404374864844251715105658146
Offset: 0

Views

Author

Seiichi Manyama, Feb 07 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp(2 * x * A(x) * exp(x * A(x))).
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A360474.
a(n) = 2 * Sum_{k=0..n} k^(n-k) * (2*n+2)^(k-1) * binomial(n,k).

A380881 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^3 * exp(x * A(x)^3) ).

Original entry on oeis.org

1, 1, 9, 163, 4541, 171781, 8231395, 478055299, 32642065433, 2562896897353, 227510655792191, 22533214047347455, 2463465770439307045, 294676777871863052173, 38284087227668033391515, 5368383942726216941810971, 808133883137288259018215345, 129988823008132636178027546257
Offset: 0

Views

Author

Seiichi Manyama, Feb 07 2025

Keywords

Crossrefs

Programs

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

Formula

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

A380973 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x*exp(3*x)) ).

Original entry on oeis.org

1, 1, 9, 115, 2213, 56781, 1825735, 70718383, 3207565737, 166830072409, 9791107408331, 640182529765395, 46152280917472669, 3637314366894167077, 311129703773921407887, 28708644100373375591191, 2842495895373573092038865, 300611288206029730901431473, 33820062046972635799385887123
Offset: 0

Views

Author

Seiichi Manyama, Feb 10 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x*A(x) * exp(3*x*A(x)) ).
a(n) = Sum_{k=0..n} (3*k)^(n-k) * (n+1)^(k-1) * binomial(n,k).
Showing 1-3 of 3 results.