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A369875 a(n) = [x^n] Product_{d|n} (x^d + 1 + 1/x^d).

%I A369875 #10 Feb 05 2024 20:57:20
%S A369875 1,1,1,1,1,4,1,1,1,1,1,19,1,1,1,1,1,11,1,11,1,1,1,85,1,1,1,6,1,64,1,1,
%T A369875 1,1,1,145,1,1,1,54,1,41,1,1,5,1,1,382,1,1,1,1,1,34,1,34,1,1,1,2425,1,
%U A369875 1,3,1,1,27,1,1,1,23,1,1943,1,1,1,1,1,20,1,225
%N A369875 a(n) = [x^n] Product_{d|n} (x^d + 1 + 1/x^d).
%C A369875 a(n) is the number of solutions to n = Sum_{d|n} c_i * d with c_i in {-1,0,1}, i=1..tau(n), tau = A000005.
%H A369875 Alois P. Heinz, <a href="/A369875/b369875.txt">Table of n, a(n) for n = 1..20000</a>
%t A369875 Table[Coefficient[Product[(x^d + 1 + 1/x^d), {d, Divisors[n]}], x, n], {n, 1, 80}]
%o A369875 (Python)
%o A369875 from collections import Counter
%o A369875 from sympy import divisors
%o A369875 def A369875(n):
%o A369875     c = {0:1}
%o A369875     for d in divisors(n,generator=True):
%o A369875         b = Counter(c)
%o A369875         for j in c:
%o A369875             a = c[j]
%o A369875             b[j+d] += a
%o A369875             b[j-d] += a
%o A369875         c = b
%o A369875     return c[n] # _Chai Wah Wu_, Feb 05 2024
%Y A369875 Cf. A000005, A033630, A083206, A316706, A369874.
%K A369875 nonn
%O A369875 1,6
%A A369875 _Ilya Gutkovskiy_, Feb 03 2024