A354849 -id:A354849 - cp's OEIS frontend

A354848 a(n) = (n-1)! * Sum_{d|n} d^(n/d + 1).

1, 5, 20, 150, 624, 9600, 36000, 811440, 6572160, 105235200, 442713600, 39437798400, 81430272000, 4956708556800, 137741700096000, 3014189418240000, 6067609067520000, 1977977787641856000, 2317659281473536000, 1297953221362237440000

Offset: 1

Seiichi Manyama, Jun 08 2022

nonn

Cf. A038048, A078308, A354849, A354851.

a[n_] := (n - 1)! * DivisorSum[n, #^(n/# + 1) &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)

PARI
```
a(n) = (n-1)!*sumdiv(n, d, d^(n/d+1));
```

my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k))))

a(n) = (n-1)! * A078308(n).
E.g.f.: -Sum_{k>0} log(1 - k * x^k).
If p is prime, a(p) = (p-1)! + p * p!.

A356524 Expansion of e.g.f. Product_{k>0} 1/(1 - k * x^k)^(1/k!).

Original entry on oeis.org

1, 1, 4, 15, 100, 565, 5946, 46039, 605256, 6646329, 103614490, 1320840631, 27185208876, 401901829069, 9042437722878, 168984439301175, 4257225193170256, 85582303577644465, 2593970612953642386, 57441717948059605927, 1862688382990615542900

Offset: 0

Seiichi Manyama, Aug 10 2022

nonn

Cf. A006906, A209902, A294462, A354849, A356487.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k!))))

a354849(n) = (n-1)!*sumdiv(n, d, d^(n/d)/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354849(j)*binomial(i-1, j-1)*v[i-j+1])); v;

a(0) = 1; a(n) = Sum_{k=1..n} A354849(k) * binomial(n-1,k-1) * a(n-k).

cp's OEIS Frontend

A354848 a(n) = (n-1)! * Sum_{d|n} d^(n/d + 1).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A356524 Expansion of e.g.f. Product_{k>0} 1/(1 - k * x^k)^(1/k!).

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula