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A363155 Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-2)).

%I A363155 #19 Jul 07 2023 06:38:14
%S A363155 0,1,0,0,3,0,0,4,0,0,5,0,2,6,0,0,7,0,0,8,5,0,9,0,0,10,0,0,17,0,0,12,0,
%T A363155 3,13,0,7,14,0,0,15,0,0,16,8,0,24,0,0,18,0,0,28,0,0,20,0,0,21,8,10,22,
%U A363155 0,0,27,0,0,24,11,0,25,0,9,26,0,0,39,0,0,28,0,0,38,0,13,40,0,0,31,0,0
%N A363155 Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-2)).
%H A363155 Seiichi Manyama, <a href="/A363155/b363155.txt">Table of n, a(n) for n = 1..10000</a>
%F A363155 a(n) = (1/5) * Sum_{d | 5*n-1, d==3 (mod 5)} (d+2).
%F A363155 G.f.: Sum_{k>0} x^(3*k-1) / (1 - x^(5*k-2))^2.
%t A363155 a[n_] := DivisorSum[5*n - 1, # + 2 &, Mod[#, 5] == 3 &]/5; Array[a, 100] (* _Amiram Eldar_, Jul 06 2023 *)
%o A363155 (PARI) a(n) = sumdiv(5*n-1, d, (d%5==3)*(d+2))/5;
%Y A363155 Cf. A359288, A363033.
%Y A363155 Cf. A363028, A364096, A364104.
%K A363155 nonn
%O A363155 1,5
%A A363155 _Seiichi Manyama_, Jul 06 2023