OFFSET
0,11
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Dean Hickerson, On the seventh order mock theta functions, Inventiones Mathematicae, 94 (1988) 661-677.
FORMULA
G.f.: g(q^2, q^7), where g(x, q) = sum for n >= 1 of q^(n(n-1))/((1-x)(1-q/x)(1-q x)(1-q^2/x)...(1-q^(n-1) x)(1-q^n/x)).
a(n) ~ exp(Pi*sqrt(2*n/21)) / (2^(3/2) * sin(2*Pi/7) * sqrt(7*n)). - Vaclav Kotesovec, Jun 14 2019
MATHEMATICA
Series[Sum[q^(7n(n-1))/Product[1-q^Abs[7k+2], {k, -n, n-1}], {n, 1, 4}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(7*k*(k-1))/Product[1-x^Abs[7*j+2], {j, -k, k-1}], {k, 1, Floor[Sqrt[nmax/7]]+1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 14 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Dean Hickerson, Dec 19 1999
STATUS
approved