A351340 a(n) = Sum_{k=0..n} n^k * k^(n-k).
1, 1, 6, 48, 516, 6955, 112686, 2132634, 46167560, 1125116901, 30481672610, 908760877244, 29565986232396, 1042354163621927, 39584173937284438, 1610922147768721590, 69940319175066857488, 3226793787576474492657, 157649292247463953189578
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..386
Programs
-
Mathematica
a[0] = 1; a[n_] := Sum[n^k * k^(n - k), {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 08 2022 *) -
PARI
a(n) = sum(k=0, n, n^k*k^(n-k));
Formula
a(n) = [x^n] Sum_{k>=0} (n*x)^k/(1 - k*x).
a(n) ~ c * n^(n + 1/2), where c = sqrt(Pi)/2. - Vaclav Kotesovec, Feb 09 2022