|
| |
|
|
A096661
|
|
Fine's numbers J(n).
|
|
3
| |
|
|
0, 0, -1, 1, -1, 1, -1, 2, -1, 0, -1, 2, -1, 0, -1, 1, -1, 0, 0, 2, -1, -1, -1, 2, 0, 0, 0, 1, -1, 0, -1, 2, -1, -1, 0, 2, 0, 0, -2, 1, -2, 0, 1, 2, -1, 0, -2, 2, 0, 0, -1, 1, -1, 0, -1, 3, -1, 0, 0, 2, -1, 0, -2, 0, -1, 1, 1, 2, -1, 0, -3, 2, 0, 0, 0, 1, -1, -1, -1, 2, -2, 0, 0, 2, 1, 1, -2, 0, -1, 0, 0, 1, -1, 0, -2, 3, 0, 0, 1, 0, -1, 0, -1, 2, -1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,8
|
|
|
REFERENCES
| N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 62, Eq. (27.1).
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.
|
|
|
MAPLE
| add( (-1)^n*q^((3*n^2+n)/2)/(1+q^n), n=1..10);
|
|
|
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
| Cf. A097042.
Sequence in context: A114114 A090787 A191329 * A199339 A098178 A007877
Adjacent sequences: A096658 A096659 A096660 * A096662 A096663 A096664
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2004
|
| |
|
|
