OFFSET
0,2
REFERENCES
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 13
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 (corrected previous b-file from G. C. Greubel)
George E. Andrews and Dean Hickerson, Ramanujan's "lost" notebook VII: The sixth order mock theta functions, Advances in Mathematics, 89 (1991) 60-105.
FORMULA
G.f.: 2 mu(q) = 1 + Sum_{n >= 0} (-1)^n q^(n+1) (1+q^n) (1-q)(1-q^3)...(1-q^(2n-1))/((1+q)(1+q^2)...(1+q^(n+1))).
a(n) ~ -(-1)^n * exp(Pi*sqrt(n/3)) / (2*sqrt(3*n)). - Vaclav Kotesovec, Jun 15 2019
MATHEMATICA
Series[1+Sum[(-1)^n q^(n+1) (1+q^n) Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+q^k, {k, 1, n+1}], {n, 0, 99}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[1 + Sum[(-1)^k * x^(k+1) * (1+x^k) * Product[1-x^j, {j, 1, 2*k-1, 2}] / Product[1+x^j, {j, 1, k+1}], {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 15 2019 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Dean Hickerson, Dec 19 1999
STATUS
approved