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.

A367879 Expansion of e.g.f. 1/(1 + 3 * x * log(1-x)).

Original entry on oeis.org

1, 0, 6, 9, 240, 1170, 25812, 244440, 5464512, 79579584, 1926411120, 37900930320, 1018338863616, 25047229315680, 752077828672128, 22027545026192160, 738063856107279360, 24935406131189352960, 927531711339595204608, 35370336293213512527360
Offset: 0

Views

Author

Seiichi Manyama, Dec 03 2023

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = 3 * n! * Sum_{k=2..n} 1/(k-1) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/2)} 3^k * k! * |Stirling1(n-k,k)|/(n-k)!.

A375684 Expansion of e.g.f. 1 / (1 - x * log(1 - x)).

Original entry on oeis.org

1, 0, -2, -3, 16, 90, -204, -4200, -5312, 254016, 1586160, -17970480, -294932736, 790115040, 54224747136, 216483714720, -10481294822400, -137535688281600, 1798183916660736, 58769251106526720, -95282580797291520, -23811620975395061760, -203282679617698222080
Offset: 0

Views

Author

Seiichi Manyama, Aug 24 2024

Keywords

Crossrefs

Programs

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

Formula

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

A375687 Expansion of e.g.f. 1 / sqrt(1 + 2 * x * log(1 - x)).

Original entry on oeis.org

1, 0, 2, 3, 44, 210, 2934, 26040, 404592, 5302584, 95029560, 1632252600, 33865401096, 712672337520, 16986980278800, 420485947572600, 11386595338156800, 322890555922925760, 9820815078397642560, 313247186941438569600, 10588974153880701225600
Offset: 0

Views

Author

Seiichi Manyama, Aug 24 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+2*x*log(1-x))))
    
  • PARI
    a001147(n) = prod(k=0, n-1, 2*k+1);
    a(n) = n!*sum(k=0, n, a001147(k)*abs(stirling(n-k, k, 1))/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} A001147(k) * |Stirling1(n-k,k)|/(n-k)!.
Showing 1-3 of 3 results.