A356541 -id:A356541 - cp's OEIS frontend

A356543 a(n) = Sum_{d|n} (d!)^(n/d-1).

1, 2, 2, 4, 2, 12, 2, 34, 38, 138, 2, 1546, 2, 5106, 15698, 54274, 2, 889314, 2, 5689090, 25448258, 39917826, 2, 2486196610, 207360002, 6227024898, 131683574018, 215393466370, 2, 14769495662082, 2, 86475697160194, 1593350982706178, 355687428161538, 648227266560002

Offset: 1

Seiichi Manyama, Aug 11 2022

nonn

Cf. A087909, A342628, A356541.

a[n_] := DivisorSum[n, (#)!^(n/# - 1) &]; Array[a, 35] (* Amiram Eldar, Aug 30 2023 *)

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

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-k!*x^k)))

G.f.: Sum_{k>=1} x^k/(1 - k! * x^k).

If p is prime, a(p) = 2.

A356542 Expansion of e.g.f. Product_{k>0} 1/(1 - k! * x^k)^(1/k!).

Original entry on oeis.org

1, 1, 4, 18, 132, 900, 11160, 100800, 1809360, 25053840, 608428800, 8610386400, 469291838400, 7110609105600, 404607162960000, 13958116204032000, 821937470818464000, 17420311428103584000, 2860701872247483264000, 60029296274562398784000

Offset: 0

Seiichi Manyama, Aug 11 2022

nonn

Cf. A209902, A356524, A356541.

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k!*x^k)^(1/k!))))

a356541(n) = sumdiv(n, d, d*d!^(n/d-1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a356541(j)*v[i-j+1]/(i-j)!)); v;

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A356541(k) * a(n-k)/(n-k)!.

cp's OEIS Frontend

A356543 a(n) = Sum_{d|n} (d!)^(n/d-1).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A356542 Expansion of e.g.f. Product_{k>0} 1/(1 - k! * x^k)^(1/k!).

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula