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A350583 Coefficients of the expansion of Sum_{n,m>=1} (-1)^m*q^(2*n*m+m)/((1+q^n)*(1-q^(2*m-1))) (odd powers only). 0

%I #6 Jan 07 2022 17:08:06

%S -1,-2,-3,-5,-4,-7,-9,-6,-11,-11,-11,-14,-15,-12,-15,-24,-14,-21,-20,

%T -16,-30,-25,-20,-27,-31,-22,-33,-31,-25,-36,-44,-28,-30,-43,-26,-50,

%U -43,-37,-47,-40,-38,-51,-53,-34,-53,-62,-38,-55,-63,-36,-74,-58,-42,-54,-64,-65,-69,-71

%N Coefficients of the expansion of Sum_{n,m>=1} (-1)^m*q^(2*n*m+m)/((1+q^n)*(1-q^(2*m-1))) (odd powers only).

%C It is conjectured that only odd powers appear in this expansion.

%H George E. Andrews, Atul Dixit, Daniel Schultz, and Ae Ja Yee, <a href="https://arxiv.org/abs/1603.04352">Overpartitions related to the mock theta function w(q)</a>, arXiv:1603.04352 [math.NT], 2016. See Y(q) p. 24.

%e G.f. = -q^3 -2*q^5 -3*q^7 -5*q^9 -4*q^11 -7*q^13 -9*q^15 -6*q^17 -11*q^19 ...

%o (PARI) lista(nn) = my(v=Vec(sum(n=1, nn, sum(m=1, nn, (-1)^m*q^(2*n*m+m)/((1+q^n)*(1-q^(2*m-1))))) + O(q^(2*nn)))); vector(#v\2, k, v[2*k-1]);

%K sign

%O 1,2

%A _Michel Marcus_, Jan 07 2022

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Last modified August 24 20:21 EDT 2024. Contains 375417 sequences. (Running on oeis4.)