A360726 Expansion of Sum_{k>0} (k * x * (1 + x^k))^k.
1, 5, 27, 264, 3125, 46741, 823543, 16778240, 387420570, 10000015625, 285311670611, 8916100729755, 302875106592253, 11112006831322817, 437893890380890625, 18446744073843770368, 827240261886336764177, 39346408075300025059665
Offset: 1
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 1..385
Programs
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Mathematica
a[n_] := DivisorSum[n, #^# * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+x^k))^k)) -
PARI
a(n) = sumdiv(n, d, d^d*binomial(d, n/d-1));
Formula
a(n) = Sum_{d|n} d^d * binomial(d,n/d-1).
If p is an odd prime, a(p) = p^p.