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%I #15 Jul 31 2023 02:25:08
%S 1,5,13,39,81,225,449,1115,2345,5373,11265,25483,53249,116497,246405,
%T 529195,1114113,2372741,4980737,10515511,22025617,46204953,96468993,
%U 201506607,419432417,872787997,1811981789,3758970975,7784628225,16108217801,33285996545,68723976779
%N Expansion of Sum_{k>0} x^k / (1 - 2 * x^k)^(k+1).
%F a(n) = Sum_{d|n} 2^(n/d-1) * binomial(d+n/d-1,d).
%F If p is prime, a(p) = 1 + p * 2^(p-1).
%t a[n_] := DivisorSum[n, 2^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 30] (* _Amiram Eldar_, Jul 31 2023 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-2*x^k)^(k+1)))
%o (PARI) a(n) = sumdiv(n, d, 2^(n/d-1)*binomial(d+n/d-1, d));
%Y Cf. A360798.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Feb 21 2023
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