OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
B. Gordon and R. J. McIntosh, Some eighth order mock theta functions, J. London Math. Soc. 62 (2000), 321-335.
FORMULA
G.f.: Sum{n >= 0} q^(n^2+n) (1+q^2)(1+q^4)...(1+q^(2n))/(1+q)(1+q^3)...(1+q^(2n+1)).
a(n) ~ (-1)^n * sqrt(1 + sqrt(2)) * exp(Pi*sqrt(n)/2) / (2^(11/4) * sqrt(n)). - Vaclav Kotesovec, Jun 14 2019
MATHEMATICA
nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)) * Product[(1 + x^(2*j)), {j, 1, k}] / Product[(1 + x^(2*j+1)), {j, 0, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 13 2019 *)
PROG
(PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^(n^2+n) * prod(k = 1, n, 1 + q^(2*k)) / prod(k = 0, n, 1 + q^(2*k+1))); Vec(gf) \\ Michel Marcus, Jun 18 2013
CROSSREFS
KEYWORD
sign
AUTHOR
Jeremy Lovejoy, Dec 19 2008
EXTENSIONS
More terms from Michel Marcus, Feb 23 2015
STATUS
approved