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%I #11 Jun 30 2023 15:36:20
%S 1,1,4,1,7,4,11,1,19,7,22,4,29,11,46,1,46,19,56,7,80,22,79,4,98,29,
%T 124,11,121,46,137,1,178,46,188,19,191,56,242,7,232,80,254,22,337,79,
%U 301,4,336,98,400,29,379,124,434,11,494,121,466,46,497,137,623,1,596,178,596,46,712,188,667,19
%N Expansion of Sum_{k>0} x^k / (1 - x^(2*k))^3.
%F G.f.: Sum_{k>0} k*(k+1)/2 * x^(2*k-1) / (1 - x^(2*k-1)).
%F a(n) = Sum_{d|n, d==1 mod 2} binomial((d+1)/2+1,2).
%t a[n_] := DivisorSum[n, Binomial[(#+1)/2+1,2] &, OddQ[#] &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (d%2==1)*binomial((d+1)/2+1, 2));
%Y Cf. A001227, A113415.
%Y Cf. A363969.
%K nonn
%O 1,3
%A _Seiichi Manyama_, Jun 30 2023
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