A064512 Ramanujan's function F_7(q).

1, 14, 42, -14, -70, -42, 70, -140, 42, 126, 210, -84, 294, -294, -84, 0, 154, -504, 378, -630, 882, -350, -252, 252, 1190, 350, 1470, -1148, 1372, -756, 0, -1680, -630, -1708, 2520, -1050, -630, -532, 3150, 0, 3570, -2940, 1750, 812, 420, -3066, 756, -3864

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc., 128 (1999), 1333-1338; F_7(q).

Formula

subs(q=-q, f)^7/subs(q=-q^7, f)+7*q^2*subs(q=-q^7, f)^7/subs(q=-q, f)+7*q*subs(q=-q, f)^3*subs(q=-q^7, f)^3, where f = A010815 = Sum_{k=-infinity, infinity} (-1)^k*q^(k*(3*k-1)/2).

Example

G.f. = 1 + 14*q + 42*q^2 - 14*q^3 - 70*q^4 - 42*q^5 + 70*q^6 - 140*q^7 + 42*q^8 + 126*q^9 + ...

Mathematica

f[q_]:= Sum[(-1)^k*q^(k*(3*k-1)/2), {k, -Infinity, Infinity}];
CoefficientList[Series[f[-q]^7/f[-q^7] +7*q^2*f[-q^7]^7/f[-q] +7*q*(f[-q] *f[-q^7])^3, {q, 0, 30}], q] (* G. C. Greubel, May 29 2019 *)

Crossrefs

Sequence in context: A366480 A199710 A214521 * A118237 A326624 A208360

Adjacent sequences: A064509 A064510 A064511 * A064513 A064514 A064515

Keyword

sign

Author

N. J. A. Sloane, Oct 06 2001

Status

approved