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A376021 a(n) = Sum_{d|n} d^(n/d - d) * binomial(n/d-1,d-1).

%I A376021 #13 Sep 06 2024 14:26:53
%S A376021 1,1,1,2,1,5,1,13,2,33,1,90,1,193,55,450,1,1295,1,2321,1216,5121,1,
%T A376021 16528,2,24577,20413,54529,1,193446,1,254721,295246,524289,376,
%U A376021 2254023,1,2359297,3897235,5329176,1,24303263,1,23986177,48404882,46137345,1,274687104,2
%N A376021 a(n) = Sum_{d|n} d^(n/d - d) * binomial(n/d-1,d-1).
%F A376021 G.f.: Sum_{k>=1} ( x^k / (1 - k*x^k) )^k.
%F A376021 If p is prime, a(p) = 1.
%o A376021 (PARI) a(n) = sumdiv(n, d, d^(n/d-d)*binomial(n/d-1, d-1));
%o A376021 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (x^k/(1-k*x^k))^k))
%o A376021 (Python)
%o A376021 from math import comb
%o A376021 from itertools import takewhile
%o A376021 from sympy import divisors
%o A376021 def A376021(n): return sum(d**((m:=n//d)-d)*comb(m-1,d-1) for d in takewhile(lambda d:d**2<=n,divisors(n))) # _Chai Wah Wu_, Sep 06 2024
%Y A376021 Cf. A376017.
%K A376021 nonn
%O A376021 1,4
%A A376021 _Seiichi Manyama_, Sep 06 2024