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 1-4 of 4 results.

A357343 E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(A(x)).

Original entry on oeis.org

0, 1, 5, 53, 878, 19904, 573984, 20112770, 829953368, 39425517072, 2119169565120, 127163052628512, 8426599011632592, 611181716437826832, 48159349246147915944, 4096752391897622411880, 374189567290578072309504, 36525100459236757201316352
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 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

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

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

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 1-4 of 4 results.