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Expansion of Sum_{k>0} k * x^k / (1 - x^(4*k-3)).
2

%I #13 Jul 05 2023 01:44:54

%S 1,3,4,5,6,7,10,9,10,11,12,18,14,15,16,17,24,19,20,21,25,30,24,25,26,

%T 27,36,29,30,38,32,42,34,35,36,37,48,39,48,41,42,54,48,45,46,47,60,58,

%U 50,51,52,66,54,55,56,66,82,59,60,61,62,78,64,65,66,78,84,69,80,71,72,90,79,75,88,77,96

%N Expansion of Sum_{k>0} k * x^k / (1 - x^(4*k-3)).

%F a(n) = (1/4) * Sum_{d | 4*n-3, d==1 (mod 4)} (d+3).

%F G.f.: Sum_{k>0} x^k / (1 - x^(4*k-3))^2.

%t a[n_] := DivisorSum[4*n - 3, # + 3 &, Mod[#, 4] == 1 &]/4; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *)

%o (PARI) a(n) = sumdiv(4*n-3, d, (d%4==1)*(d+3))/4;

%Y Cf. A359227.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 04 2023