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Expansion of Sum_{k>0} k * x^k / (1 - x^(2*k-1)).
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%I #21 Nov 30 2024 12:29:26

%S 1,3,4,5,8,7,8,14,10,11,18,13,17,22,16,17,26,26,20,30,22,23,42,25,30,

%T 38,28,38,42,31,32,55,44,35,50,37,38,65,50,41,63,43,56,62,46,58,66,62,

%U 50,81,52,53,100,55,56,78,58,74,94,74,68,86,80,65,90,67,82,124,70,71,98,86,92,117,76,77

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

%H Antti Karttunen, <a href="/A364063/b364063.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = (1/2) * Sum_{d | 2*n-1} (d+1) = A007503(2*n-1)/2.

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

%F a(n) = A336840(A064216(n)). - _Antti Karttunen_, Nov 30 2024

%t a[n_] := DivisorSum[2*n - 1, # + 1 &]/2; Array[a, 100] (* _Amiram Eldar_, Jul 04 2023*)

%o (PARI) a(n) = sumdiv(2*n-1, d, d+1)/2;

%Y Cf. A000005, A000203, A007503, A064216, A336840.

%Y Cf. A364066, A364085.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 04 2023