OFFSET
0,3
COMMENTS
See Dragonette for the definition of f(q) and A(n). - N. J. A. Sloane, Sep 24 2022
REFERENCES
G. E. Andrews, The theory of partitions, Cambridge University Press, Cambridge, 1998, page 82, Example 5. MR1634067 (99c:11126). [The Gamma function used by Andrews is the classical Gamma function, which is different from the gamma(n) of this sequence. - N. J. A. Sloane, Sep 24 2022]
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.
L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500. Enlargement of a portion of page 496 in order to show correct spelling of gamma(n).
Eric Weisstein's World of Mathematics, Mock Theta Function.
FORMULA
G.f.: 1 + 4 * Sum_{k>0} (-1)^k * x^(k*(3*k + 1)/2) / (1 + x^k). - Michael Somos, Jun 19 2003
a(n) = 4 * A096661(n) unless n=0.
EXAMPLE
G.f. = 1 - 4*x^2 + 4*x^3 - 4*x^4 + 4*x^5 - 4*x^6 + 8*x^7 - 4*x^8 - 4*x^10 + 8*x^11 - 4*x^12 - ...
MATHEMATICA
a[ n_]:= SeriesCoefficient[1 +4 *Sum[(-1)^k*x^(k*(3*k+1)/2)/(1+x^k), {k, Quotient[Sqrt[1 +24*n] - 1, 6]}], {x, 0, n}]; (* Michael Somos, Apr 08 2015 *)
PROG
(PARI) {a(n) = if( n<1, n==0, 4 * 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,changed
AUTHOR
Eric W. Weisstein, Aug 28 2001
EXTENSIONS
Entry revised by Michael Somos, Mar 13 2006
Deleted edit that tried to change gamma(n) to Gamma(n), and restored original definition. - N. J. A. Sloane, Sep 24 2022
STATUS
approved