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 1-5 of 5 results.

A370993 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x)) ).

Original entry on oeis.org

1, 0, 2, 3, 80, 450, 11424, 133140, 3670400, 68303088, 2123212320, 54742984560, 1938915574848, 63653459126400, 2565847637273088, 101718189575664480, 4637150408792355840, 214393171673968519680, 10962579011721928980480, 577166004742408670937600
Offset: 0

Views

Author

Seiichi Manyama, Mar 06 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x)))/x))
    
  • PARI
    a(n) = sum(k=0, n\2, (n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n+k)! * |Stirling1(n-k,k)|/(n-k)!.

A376344 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2)) ).

Original entry on oeis.org

1, 0, 0, 6, 0, 60, 2880, 1680, 201600, 8074080, 19958400, 1824197760, 69854400000, 436929292800, 36099561738240, 1392369634656000, 17026966410854400, 1344523178718720000, 54023115000830976000, 1095484919871908966400, 84994409643640713216000, 3650011125774294048768000, 109122812080533877712486400
Offset: 0

Views

Author

Seiichi Manyama, Sep 21 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2)))/x))
    
  • PARI
    a(n) = sum(k=0, n\2, (2*n-2*k)!*abs(stirling(k, n-2*k, 1))/k!)/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (2*n-2*k)! * |Stirling1(k,n-2*k)|/k!.

A370995 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^3*log(1-x)) ).

Original entry on oeis.org

1, 0, 0, 0, 24, 60, 240, 1260, 209664, 2056320, 20476800, 221205600, 19370292480, 406935809280, 7376151444480, 131868581644800, 8376837844193280, 282378273124147200, 7891890567682867200, 207283550601631795200, 11520967360247698636800
Offset: 0

Views

Author

Seiichi Manyama, Mar 06 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^3*log(1-x)))/x))
    
  • PARI
    a(n) = sum(k=0, n\4, (n+k)!*abs(stirling(n-3*k, k, 1))/(n-3*k)!)/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n+k)! * |Stirling1(n-3*k,k)|/(n-3*k)!.

A371138 E.g.f. satisfies A(x) = 1 - x^2*A(x)^2*log(1 - x*A(x)).

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 2340, 18648, 154560, 5767200, 95911200, 1438778880, 48014778240, 1228487644800, 27997623029376, 972327510000000, 32550437645107200, 1006902423902269440, 38894136241736494080, 1569697954634035537920, 61093442927846310912000
Offset: 0

Views

Author

Seiichi Manyama, Mar 12 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!^2*sum(k=0, n\3, abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-k+1)!));

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/3)} |Stirling1(n-2*k,k)|/( (n-2*k)! * (n-k+1)! ).
E.g.f.: (1/x) * Series_Reversion( x/(1 - x^2*log(1 - x)) ). - Seiichi Manyama, Sep 19 2024

A371302 E.g.f. satisfies A(x) = 1/(1 + x^2*log(1 - x*A(x))).

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 1620, 13608, 117600, 2924640, 49603680, 782147520, 19083936960, 463369645440, 10836652514688, 304533583200000, 9218842256332800, 281872333420554240, 9421579421176089600, 338543319734116116480, 12590519274541116518400
Offset: 0

Views

Author

Seiichi Manyama, Mar 18 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\3, (n-k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-2*k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-k)! * |Stirling1(n-2*k,k)|/( (n-2*k)! * (n-2*k+1)! ).
Showing 1-5 of 5 results.