A368505 a(n) = Sum_{k=0..n} n^(n-k) * k^n.

1, 1, 6, 60, 900, 18945, 536046, 19750864, 923023368, 53456736825, 3758407535410, 315059660550756, 31005946105301388, 3535337355213234025, 461813139285801522870, 68448013078470849802560, 11415281142784979557384208, 2126537819755999634260404945

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / (exp(n) * (log(n))^(n+1)). - Vaclav Kotesovec, Dec 28 2023

Mathematica

Join[{1}, Table[Sum[n^(n-k) k^n, {k, 0, n}], {n, 20}]] (* Harvey P. Dale, May 17 2026 *)

Prog

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

Crossrefs

Main diagonal of A368504.

Cf. A303991, A349836.

Sequence in context: A064815 A387964 A331120 * A296956 A366335 A308332

Adjacent sequences: A368502 A368503 A368504 * A368506 A368507 A368508

Keyword

nonn

Author

Seiichi Manyama, Dec 27 2023

Status

approved