A349964 -id:A349964 - cp's OEIS frontend

A349966 a(n) = Sum_{k=0..n} (k * (n-k))^n.

1, 0, 1, 16, 418, 17600, 1086979, 92223488, 10292241540, 1462309109760, 257739952352133, 55188518041440256, 14111052911099343782, 4246668467339066589184, 1485904567816768099571207, 598145009954138900489830400

Offset: 0

Seiichi Manyama, Dec 07 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..240

Cf. A033455, A100262, A145216, A165817, A306548, A349964, A349965.

a[0] = 1; a[n_] := Sum[(k*(n - k))^n, {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Dec 07 2021 *)

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

a(n) = [x^n] (Sum_{k=0..n} k^n * x^k)^2.

a(n) ~ sqrt(Pi) * n^(2*n + 1/2) / 2^(2*n + 1). - Vaclav Kotesovec, Dec 07 2021

A349969 a(n) = Sum_{k=0..n} (k*n)^(n-k).

Original entry on oeis.org

1, 1, 3, 16, 141, 1871, 34951, 873174, 27951929, 1107415549, 52891809491, 2987861887924, 196828568831365, 14950745148070499, 1296606974501951743, 127238563043551898986, 14012626653816435643633, 1719136634276882827095009, 233448782800118609096218891

Offset: 0

Seiichi Manyama, Dec 07 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..284

Cf. A026898, A155956, A349964, A349970.

a[n_] := Sum[If[k == n == 0, 1, (k*n)^(n - k)], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 07 2021 *)

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

a(n) = [x^n] Sum_{k>=0} x^k/(1 - n*k * x).

a(n) ~ sqrt(2*Pi/(n*(1 + LambertW(exp(1)*n^2)))) * (n^2/LambertW(exp(1)*n^2))^(n + 1/2 - n/LambertW(exp(1)*n^2)). - Vaclav Kotesovec, Dec 07 2021

cp's OEIS Frontend

A349966 a(n) = Sum_{k=0..n} (k * (n-k))^n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula