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A294407
Expansion of 1/(1 + Sum_{i>=1} q^(i^2)/Product_{j=1..i} (1 + q^j)^2).
5
1, -1, 3, -8, 20, -51, 132, -339, 868, -2228, 5720, -14676, 37659, -96644, 248004, -636413, 1633144, -4190920, 10754580, -27598012, 70821032, -181738372, 466370429, -1196782952, 3071141180, -7881051500, 20224069573, -51898276576, 133179482008, -341760374284, 877013123076, -2250559385788
OFFSET
0,3
COMMENTS
Convolution inverse of the 3rd order mock theta function f(q) (A000025).
LINKS
Eric Weisstein's World of Mathematics, Mock Theta Function
FORMULA
G.f.: 1/(1 + Sum_{i>=1} q^(i^2)/Product_{j=1..i} (1 + q^j)^2).
MAPLE
N:= 50: # to get a(0)..a(N)
g:= 1/(1+add(q^(i^2)/mul(1+q^j, j=1..i)^2, i=1..floor(sqrt(N)))):
S:= series(g, q, N+1):
seq(coeff(S, q, n), n=0..N); # Robert Israel, Nov 06 2017
MATHEMATICA
nmax = 31; CoefficientList[Series[1/(1 + Sum[q^(i^2)/Product[(1 + q^j)^2, {j, 1, i}], {i, 1, nmax}]), {q, 0, nmax}], q]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 30 2017
STATUS
approved