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.

A370580 a(n) = (n-1)! * Sum_{d|n} d/(d-1)!.

Original entry on oeis.org

1, 3, 5, 22, 29, 546, 727, 18488, 100809, 1164250, 3628811, 208232652, 479001613, 18741602894, 236107872015, 4796881689616, 20922789888017, 1618457192352018, 6402373705728019, 471378116297088020, 6105908234409984021, 153272981387362636822
Offset: 1

Views

Author

Seiichi Manyama, Feb 23 2024

Keywords

Crossrefs

Programs

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

Formula

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

A370603 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).

Original entry on oeis.org

1, 4, 9, 40, 125, 936, 5047, 42848, 367929, 3668500, 39916811, 480577032, 6227020813, 87197480384, 1307761815375, 20923593490816, 355687428096017, 6402405005606628, 121645100408832019, 2432903231908929800, 51090944698284691221, 1124000756238680570272
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 * A370608(n).
If p is prime, a(p) = p + p!.
E.g.f.: Sum_{k>0} x^k * exp(x^k/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).

A370581 a(n) = n! * Sum_{d|n} d/(d! * (n/d)!).

Original entry on oeis.org

1, 3, 4, 17, 6, 307, 8, 5049, 30250, 105851, 12, 25945933, 14, 77837775, 14529715216, 147891744017, 18, 13435316294419, 20, 7606841430988821, 16895152834560022, 183030822374423, 24, 387276381308571955225, 5385836820601036800026, 485735643993600027
Offset: 1

Views

Author

Seiichi Manyama, Feb 23 2024

Keywords

Crossrefs

Programs

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

Formula

If p is prime, a(p) = 1 + p.
E.g.f.: Sum_{k>0} x^k/k! * exp(x^k).
Showing 1-4 of 4 results.