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A376015 a(n) = Sum_{d|n} d^n * binomial(n/d,d).

%I A376015 #19 Sep 06 2024 14:08:12
%S A376015 1,2,3,20,5,198,7,1544,19692,10250,11,2187216,13,344078,143489085,
%T A376015 4296802320,17,7757846982,19,5497605324820,366112362126,230686742,23,
%U A376015 4237941811999056,298023223876953150,5234491418,640550188738935,2522015815755104284
%N A376015 a(n) = Sum_{d|n} d^n * binomial(n/d,d).
%H A376015 Seiichi Manyama, <a href="/A376015/b376015.txt">Table of n, a(n) for n = 1..724</a>
%F A376015 G.f.: Sum_{k>=1} ((k*x)^k)^k / (1 - (k*x)^k)^(k+1).
%F A376015 If p is prime, a(p) = p.
%o A376015 (PARI) a(n) = sumdiv(n, d, d^n*binomial(n/d, d));
%o A376015 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, ((k*x)^k)^k/(1-(k*x)^k)^(k+1)))
%o A376015 (Python)
%o A376015 from math import comb
%o A376015 from itertools import takewhile
%o A376015 from sympy import divisors
%o A376015 def A376015(n): return sum(d**n*comb(n//d,d) for d in takewhile(lambda d:d**2<=n,divisors(n))) # _Chai Wah Wu_, Sep 06 2024
%Y A376015 Cf. A023887, A338685.
%K A376015 nonn
%O A376015 1,2
%A A376015 _Seiichi Manyama_, Sep 06 2024