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.

A357345 E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(3 * A(x)).

Original entry on oeis.org

0, 1, 9, 173, 5226, 216564, 11429592, 733443990, 55447217928, 4826605609584, 475490102407200, 52299789903627408, 6353202640983827472, 844774875973448667792, 122040471544637793494760, 19034141943046836097099080, 3187643959565686909679931648
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, (n+3*k)^(k-1)*abs(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) * (1 - exp(-x * exp(-3*x))) ). - Seiichi Manyama, Sep 09 2024

A357344 E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(2 * A(x)).

Original entry on oeis.org

0, 1, 7, 104, 2422, 77304, 3141108, 155155580, 9027723248, 604793361744, 45851401106880, 3880989671623008, 362790690552990720, 37120807927059003744, 4126551430278515989632, 495243629308215934662720, 63819561948443247132306432, 8789113187481077533462305024
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, (n+2*k)^(k-1)*abs(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) * (1 - exp(-x * exp(-2*x))) ). - Seiichi Manyama, Sep 09 2024

A357422 E.g.f. satisfies A(x) * exp(A(x)) = -log(1 - x * exp(A(x))).

Original entry on oeis.org

0, 1, 1, 5, 34, 324, 3936, 58190, 1014056, 20354544, 462472800, 11733507312, 328809013776, 10086567702288, 336184985751720, 12097485061713480, 467445074411402496, 19303428522591336960, 848420150154305711616, 39543441411041750547648
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, (n-k)^(k-1)*abs(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) * (1 - exp(-x * exp(x))) ). - Seiichi Manyama, Sep 09 2024
Showing 1-3 of 3 results.