A356687 -id:A356687 - cp's OEIS frontend

A356688 a(n) = n! * Sum_{k=0..n} k^(3*n)/k!.

1, 1, 66, 21225, 18952156, 36175231585, 126556309395486, 733064060959310689, 6540867625730306094360, 85180334386943946887707617, 1552697061493449955344530003290, 38315904135534199560725372265381721, 1245605749857294018587318829355458646068

Offset: 0

Seiichi Manyama, Aug 23 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..149

Cf. A256016, A356687.

Cf. A337001, A349901, A356673.

a[n_] := n! * Sum[k^(3*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 13, 0] (* Amiram Eldar, Aug 23 2022 *)

PARI
```
a(n) = n!*sum(k=0, n, k^(3*n)/k!);
```

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*x)^k/(k!*(1-k^3*x)))))

E.g.f.: Sum_{k>=0} (k^3 * x)^k / (k! * (1 - k^3 * x)).

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

Original entry on oeis.org

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)).

cp's OEIS Frontend

A356688 a(n) = n! * Sum_{k=0..n} k^(3*n)/k!.

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula