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A376020 a(n) = Sum_{d|n} d^(n/d) * binomial(n/d-1,d-1).

%I A376020 #15 Sep 06 2024 14:43:00
%S A376020 1,1,1,5,1,17,1,49,28,129,1,564,1,769,1459,2049,1,11387,1,13313,32806,
%T A376020 20481,1,223798,3126,98305,551125,540673,1,2662642,1,3276801,7971616,
%U A376020 2097153,1171876,48412424,1,9437185,105225319,121675204,1,416694239,1,591396865
%N A376020 a(n) = Sum_{d|n} d^(n/d) * binomial(n/d-1,d-1).
%F A376020 G.f.: Sum_{k>=1} ( k*x^k / (1 - k*x^k) )^k.
%F A376020 If p is prime, a(p) = 1.
%o A376020 (PARI) a(n) = sumdiv(n, d, d^(n/d)*binomial(n/d-1, d-1));
%o A376020 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k/(1-k*x^k))^k))
%o A376020 (Python)
%o A376020 from math import comb
%o A376020 from itertools import takewhile
%o A376020 from sympy import divisors
%o A376020 def A376020(n): return sum(d**(m:=n//d)*comb(m-1,d-1) for d in takewhile(lambda d:d**2<=n,divisors(n))) # _Chai Wah Wu_, Sep 06 2024
%Y A376020 Cf. A376016.
%K A376020 nonn
%O A376020 1,4
%A A376020 _Seiichi Manyama_, Sep 06 2024