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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
-1, -2, -3, -5, -4, -7, -9, -6, -11, -11, -11, -14, -15, -12, -15, -24, -14, -21, -20, -16, -30, -25, -20, -27, -31, -22, -33, -31, -25, -36, -44, -28, -30, -43, -26, -50, -43, -37, -47, -40, -38, -51, -53, -34, -53, -62, -38, -55, -63, -36, -74, -58, -42, -54, -64, -65, -69, -71
OFFSET
1,2
COMMENTS
It is conjectured that only odd powers appear in this expansion.
LINKS
George E. Andrews, Atul Dixit, Daniel Schultz, and Ae Ja Yee, Overpartitions related to the mock theta function w(q), arXiv:1603.04352 [math.NT], 2016. See Y(q) p. 24.
EXAMPLE
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 ...
PROG
(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]);
CROSSREFS
Sequence in context: A193973 A245057 A127521 * A102399 A118318 A245707
KEYWORD
sign
AUTHOR
Michel Marcus, Jan 07 2022
STATUS
approved