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Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k*(k+1)) / (1 - x^k).
1

%I #5 May 21 2024 05:30:41

%S 0,1,1,1,1,-3,1,-3,1,-3,1,6,1,-3,10,-3,1,6,1,-19,10,-3,1,-10,1,-3,10,

%T -19,1,31,1,-19,10,-3,26,-10,1,-3,10,6,1,-30,1,-19,35,-3,1,-46,1,22,

%U 10,-19,1,-30,26,30,10,-3,1,-21,1,-3,59,-19,26,-30,1,-19,10,71

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

%F a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(d+1) * d^2.

%t nmax = 70; CoefficientList[Series[Sum[(-1)^(k + 1) k^2 x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A056924, A064027, A070039, A321543, A333809, A333810, A339353, A344300, A372625, A373031.

%K sign

%O 1,6

%A _Ilya Gutkovskiy_, May 20 2024