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A376017 a(n) = Sum_{d|n} d^(n/d - d) * binomial(n/d,d).

%I A376017 #17 Sep 06 2024 14:08:02
%S A376017 1,2,3,5,5,12,7,32,10,90,11,264,13,686,105,1809,17,5166,19,11560,2856,
%T A376017 28182,23,81456,26,159770,61263,375004,29,1122660,31,1984032,1082598,
%U A376017 4456482,560,14486329,37,22413350,16888053,50674560,41,174582072,43,247627820,241884450
%N A376017 a(n) = Sum_{d|n} d^(n/d - d) * binomial(n/d,d).
%H A376017 Seiichi Manyama, <a href="/A376017/b376017.txt">Table of n, a(n) for n = 1..5000</a>
%F A376017 G.f.: Sum_{k>=1} x^(k^2) / (1 - k*x^k)^(k+1).
%F A376017 If p is prime, a(p) = p.
%o A376017 (PARI) a(n) = sumdiv(n, d, d^(n/d-d)*binomial(n/d, d));
%o A376017 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, x^k^2/(1-k*x^k)^(k+1)))
%o A376017 (Python)
%o A376017 from math import comb
%o A376017 from itertools import takewhile
%o A376017 from sympy import divisors
%o A376017 def A376017(n): return sum(d**((m:=n//d)-d)*comb(m,d) for d in takewhile(lambda d:d**2<=n,divisors(n))) # _Chai Wah Wu_, Sep 06 2024
%Y A376017 Cf. A318636.
%K A376017 nonn
%O A376017 1,2
%A A376017 _Seiichi Manyama_, Sep 06 2024