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

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

Offset: 0

Author

Seiichi Manyama, Dec 07 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A026898, A155956, A349964, A349970.

Programs

Mathematica

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));

Formula

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