A061711 -id:A061711 - cp's OEIS frontend

A368573 a(n) = Sum_{k=0..n} k! * k^k.

1, 2, 10, 172, 6316, 381316, 33973636, 4184630356, 680641979476, 141267789027796, 36429267789027796, 11425158161234192596, 4282251538636575402196, 1890291840090813125264596, 970616058694975134467523796, 573593232413546537634467523796, 386530943604347679737893326531796

Offset: 0

Seiichi Manyama, Dec 31 2023

Partial sums of A061711.
Cf. A058006, A112368, A112370.
Cf. A367011, A367012, A368561.

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

a(n) ~ n! * n^n. - Vaclav Kotesovec, Jan 13 2024

A369569 a(n) = (n-1)! * n^n.

Original entry on oeis.org

1, 4, 54, 1536, 75000, 5598720, 592950960, 84557168640, 15620794116480, 3628800000000000, 1035338990313196800, 355902198372945100800, 145077660657859734604800, 69194697632491737238732800, 38174841090323437500000000000, 24122334398245883325016178688000

Offset: 1

Thomas Scheuerle, Jan 26 2024

nonn

The number of ways n different tags can be assigned to different nodes of an unspecified labeled rooted tree with n nodes. (This therefore includes the choice of one of the n^(n-1) labeled rooted trees.) In this description, we differentiate between labels and tags: we view the labels together with the root as part of the labeled rooted tree's definition, but the tags as an assignment in relation to the labels that is independent of the root.

Is this, equivalently, the number of doubly labeled rooted trees?

			The 4 labeled rooted trees with two nodes and two tags assigned are:
.
  R        R
  L1--L2   L1--L2
  T1  T2   T2  T1
.
       R        R
  L1--L2   L1--L2
  T1  T2   T2  T1
.

Cf. A000312, A000169, A061711.

Maple
```
seq(n^n*factorial(n-1), n=1..16)
```
Mathematica
```
Table[n^n*(n-1)!, {n, 1, 16}]
```
PARI
```
a(n) = (n-1)!*n^n
```

a(n) = n! * n^(n-1).
a(n) = Integral_{x>=0} x^(n-1) * exp(-x/n) dx.
a(n) = n! * [x^n] (1/n)*sinh(n*x)^n. - Stefano Spezia, Feb 21 2024

cp's OEIS Frontend

A368573 a(n) = Sum_{k=0..n} k! * k^k.

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A369569 a(n) = (n-1)! * n^n.

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Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica

PARI

Formula