OFFSET
0,2
COMMENTS
REFERENCES
B. C. Berndt, Ramanujan's Notebooks Part V, Springer-Verlag, 1998.
FORMULA
Coefficients of 1/3 of power series in equation (13.23), page 179, [Berndt 1998]
A051273(n) = 3*a(n).
a(n) ~ (-1)^n * 64 * Pi^5 * n * exp(Pi*(3*n+1)/3^(3/2)) / Gamma(1/6)^6. - Vaclav Kotesovec, Nov 08 2019
EXAMPLE
G.f. = 1 - 14*x + 131*x^2 - 1080*x^3 + 8333*x^4 - 61580*x^5 + ...
G.f. = q - 14*q^4 + 131*q^7 - 1080*q^10 + 8333*q^13 - 61580*q^16 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[x]^2 QPochhammer[x^3]^4 / (QPochhammer[x]^3 + 9 x QPochhammer[x^9]^3)^2, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n < 0, 0, A = x * O(x^n); A = ((eta(x + A) * eta(x^3 + A)) / (eta(x^2 + A) * eta(x^6 + A)))^2; polcoeff( 1 / (A + x * 16/A^2), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Nov 02 2019
STATUS
approved