OFFSET
0,8
REFERENCES
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 62, Eq. (27.1).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500. See page 496.
FORMULA
G.f.: Sum_{n >= 1} (-1)^n*q^((3*n^2+n)/2)/(1+q^n).
Dragonette's gamma(n) = A064053(n) = 4*a(n) if n>0.
EXAMPLE
G.f. = - x^2 + x^3 - x^4 + x^5 - x^6 + 2*x^7 - x^8 - x^10 + 2*x^11 - x^12 + ...
MAPLE
add( (-1)^n*q^((3*n^2+n)/2)/(1+q^n), n=1..10);
MATHEMATICA
a[n_]:= SeriesCoefficient[Sum[(-1)^k*q^((3*k^2 + k)/2)/(1 + q^k), {k, 1, 2*nmax}], {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 18 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=1, (sqrtint(24*n + 1) - 1) \ 6, (-1)^k * x^((3*k^2 + k)/2) / (1 + x^k), x * O(x^n)), n))}; /* Michael Somos, Mar 13 2006 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Sep 15 2004
STATUS
approved