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.

A357347 E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(2 * A(x)).

Original entry on oeis.org

0, 1, 7, 103, 2385, 75756, 3064239, 150689953, 8729691693, 582299930167, 43956280309659, 3704637865439380, 344825037782332457, 35131983926187957173, 3888817094785288023367, 464724955485177444101895, 59631976064836824117227621, 8177487264101392841050876136
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2022

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=1..n} (n+2*k)^(k-1) * Stirling2(n,k).
E.g.f.: Series_Reversion( exp(-x) * log(1 + x * exp(-2*x)) ). - Seiichi Manyama, Sep 09 2024

A357346 E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(A(x)).

Original entry on oeis.org

0, 1, 5, 52, 849, 18996, 540986, 18726247, 763480675, 35837071558, 1903538106065, 112880374866172, 7392418912962210, 529898419942327801, 41266682731537698181, 3469461853041348996044, 313200848521114144611273, 30215925892728362737156556
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2022

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=1..n} (n+k)^(k-1) * Stirling2(n,k).
E.g.f.: Series_Reversion( exp(-x) * log(1 + x * exp(-x)) ). - Seiichi Manyama, Sep 09 2024

A357348 E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(3 * A(x)).

Original entry on oeis.org

0, 1, 9, 172, 5181, 214196, 11279542, 722242795, 54482959375, 4732518179422, 465226448603533, 51061919634063284, 6189640391474229790, 821277806639279795053, 118394082630978607655201, 18426248367244130561233924, 3079294928622816257125500821
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, (n+3*k)^(k-1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=1..n} (n+3*k)^(k-1) * Stirling2(n,k).
E.g.f.: Series_Reversion( exp(-x) * log(1 + x * exp(-3*x)) ). - Seiichi Manyama, Sep 09 2024
Showing 1-3 of 3 results.