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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..240
Programs
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Mathematica
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);
Formula
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