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.

A370579 a(n) = n! * Sum_{d|n} 1/(d-1)!.

Original entry on oeis.org

1, 4, 9, 52, 125, 1806, 5047, 87368, 544329, 7408810, 39916811, 1281329292, 6227020813, 174477663374, 2015997984015, 45336862771216, 355687428096017, 16059446167564818, 121645100408832019, 5372665305815808020, 76707372899469312021, 2248001765299683993622
Offset: 1

Views

Author

Seiichi Manyama, Feb 23 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sumdiv(n, d, 1/(d-1)!);
    
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*exp(x^k))))

Formula

a(n) = n * A087906(n).
If p is prime, a(p) = p + p!.
E.g.f.: Sum_{k>0} x^k * exp(x^k).

A370602 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)^(d-1)).

Original entry on oeis.org

1, 4, 9, 40, 125, 1056, 5047, 51248, 383049, 4364020, 39916811, 576885552, 6227020813, 99634224704, 1334500527375, 23592657488416, 355687428096017, 7202890599354468, 121645100408832019, 2679832071577681040, 51612375654647808021, 1226182612423511392672
Offset: 1

Views

Author

Seiichi Manyama, Feb 23 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sumdiv(n, d, 1/((d-1)!*(n/d)^(d-1)));
    
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*exp(x^k/k))))

Formula

a(n) = n * A005225(n).
If p is prime, a(p) = p + p!.
E.g.f.: Sum_{k>0} x^k * exp(x^k/k).

A370608 a(n) = (n-1)! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).

Original entry on oeis.org

1, 2, 3, 10, 25, 156, 721, 5356, 40881, 366850, 3628801, 40048086, 479001601, 6228391456, 87184121025, 1307724593176, 20922789888001, 355689166978146, 6402373705728001, 121645161595446490, 2432902128489747201, 51090943465394571376, 1124000727777607680001
Offset: 1

Views

Author

Seiichi Manyama, Feb 23 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = (n-1)!*sumdiv(n, d, 1/((d-1)!*(n/d)!^(d-1)));
    
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k-1)!*(exp(x^k/k!)-1))))

Formula

If p is prime, a(p) = 1 + (p-1)!.
E.g.f.: Sum_{k>0} (k-1)! * (exp(x^k/k!)-1).
Showing 1-3 of 3 results.