A356674 -id:A356674 - cp's OEIS frontend

A356689 a(n) = n! * Sum_{k=0..n} k^(k*n)/k!.

1, 2, 20, 19887, 4297096180, 298028721722131825, 10314430386434427534836297166, 256923580889667624113335512704714686054849, 6277101737079381675512518990977258744796239498871290255000

Offset: 0

Seiichi Manyama, Aug 23 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..26

Cf. A256016, A356687, A356688.

Cf. A349886, A356674.

PARI
```
a(n) = n!*sum(k=0, n, k^(k*n)/k!);
```

my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^k*x)^k/(k!*(1-k^k*x)))))

E.g.f.: Sum_{k>=0} (k^k * x)^k / (k! * (1 - k^k * x)).

A358688 a(n) = n! * Sum_{k=0..n} k^(k * (n-k)) / (n-k)!.

Original entry on oeis.org

1, 2, 5, 34, 869, 75866, 28213327, 39049033346, 256215628707257, 7710689746589777938, 1063776147486867074877851, 870059224717752809087935599002, 3104894940194751778363241199111802885, 77521065749331962430758061530260243383954602

Offset: 0

Seiichi Manyama, Nov 26 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..51

Cf. A006153, A193421, A358687.

Cf. A349893, A356674.

Table[1 + n!*Sum[k^(k*(n-k))/(n-k)!, {k, 1, n}], {n, 0, 12}] (* Vaclav Kotesovec, Nov 27 2022 *)

a(n) = n!*sum(k=0, n, k^(k*(n-k))/(n-k)!);

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k*exp(x)^k^k)))

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1-k^k*x)^(k+1)))

E.g.f.: Sum_{k>=0} x^k * exp(k^k * x).

G.f.: Sum_{k>=0} k! * x^k / (1 - k^k * x)^(k+1).

cp's OEIS Frontend

A356689 a(n) = n! * Sum_{k=0..n} k^(k*n)/k!.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula

A358688 a(n) = n! * Sum_{k=0..n} k^(k * (n-k)) / (n-k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

PARI

Formula