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.

A357350 E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(2 * A(x)).

Original entry on oeis.org

0, 1, 5, 62, 1210, 32464, 1109988, 46159364, 2261784880, 127625290704, 8150589862080, 581192861530368, 45772039038334464, 3945903751253912928, 369585982325018567808, 37372951572516507717120, 4057994343926975346772992, 470900282395259211311765760
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, 1));

Formula

a(n) = Sum_{k=1..n} (n+2*k)^(k-1) * Stirling1(n,k).
E.g.f.: Series_Reversion( exp(-x) * (exp(x * exp(-2*x)) - 1) ). - Seiichi Manyama, Sep 10 2024

A357351 E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(3 * A(x)).

Original entry on oeis.org

0, 1, 7, 119, 3186, 117204, 5493672, 313159146, 21032534856, 1626654909168, 142381874412000, 13915051276560048, 1501957674420194736, 177456652252068578544, 22779601954164759020184, 3156967397734735846493880, 469790199951668305705905408
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, 1));

Formula

a(n) = Sum_{k=1..n} (n+3*k)^(k-1) * Stirling1(n,k).
E.g.f.: Series_Reversion( exp(-x) * (exp(x * exp(-3*x)) - 1) ). - Seiichi Manyama, Sep 10 2024

A357423 E.g.f. satisfies A(x) * exp(A(x)) = log(1 + x * exp(A(x))).

Original entry on oeis.org

0, 1, -1, -1, 10, 4, -384, 818, 29800, -205200, -3612000, 56042832, 556589232, -19091774352, -70128589608, 8044430218680, -25379500932864, -4055729067351552, 48310659088501248, 2334746679051721536, -58078273556262804480, -1420062892415588203776
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2022

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=1..n} (n-k)^(k-1) * Stirling1(n,k).
E.g.f.: Series_Reversion( exp(-x) * (exp(x * exp(x)) - 1) ). - Seiichi Manyama, Sep 10 2024
Showing 1-3 of 3 results.