A360831 Expansion of Sum_{k>0} (k * x)^k / (1 - (k * x)^k)^(k+1).
1, 6, 30, 308, 3130, 49962, 823550, 17107464, 387617328, 10058609120, 285311670622, 8931600297696, 302875106592266, 11117432610599574, 437894531752211760, 18449277498826162192, 827240261886336764194, 39347911865350001626164
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, #^n * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-(k*x)^k)^(k+1))) -
PARI
a(n) = sumdiv(n, d, d^n*binomial(d+n/d-1, d));
Formula
a(n) = Sum_{d|n} d^n * binomial(d+n/d-1,d).
If p is prime, a(p) = p + p^p.