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 1-2 of 2 results.

A379701 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) / (1 + x*exp(2*x)) ).

Original entry on oeis.org

1, 0, 3, 2, 113, 304, 13747, 83600, 3590337, 38193920, 1650383171, 26535997696, 1186785903217, 26244849422336, 1234578346302771, 35176362803984384, 1757110507998276353, 61533880908307038208, 3281634015502670522371, 136392534106346468999168
Offset: 0

Views

Author

Seiichi Manyama, Dec 30 2024

Keywords

Crossrefs

Programs

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

Formula

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

A379847 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(3*x)) ).

Original entry on oeis.org

1, 2, 17, 259, 5773, 171021, 6342937, 283094309, 14785425081, 885090944809, 59765476266061, 4494836808752049, 372655043070926821, 33769844474642217293, 3320996349535681398849, 352267766021524028011981, 40091829710459334010532593, 4873329774181782935197522641
Offset: 0

Views

Author

Seiichi Manyama, Jan 04 2025

Keywords

Crossrefs

Programs

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

Formula

a(n) = (n!/(n+1)) * Sum_{k=0..n} (4*n-3*k+1)^k * binomial(n+1,n-k)/k!.
E.g.f. A(x) satisfies A(x) = exp(x*A(x)) / ( 1 - x*exp(4*x*A(x)) ). - Seiichi Manyama, Feb 04 2025
Showing 1-2 of 2 results.