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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Convolution inverse of the 3rd order mock theta function f(q) (A000025).

LINKS

Robert Israel, Table of n, a(n) for n = 0..2441

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

Cf. A000025, A000039, A000199, A010815.

Sequence in context: A140662 A174198 A077997 * A295346 A027220 A305823

Adjacent sequences:  A294404 A294405 A294406 * A294408 A294409 A294410

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Oct 30 2017

STATUS

approved

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Last modified September 25 00:02 EDT 2020. Contains 337333 sequences. (Running on oeis4.)