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_5(q).
FORMULA
subs(q=-q, f)^5/subs(q=-q^5, f)+5*q*subs(q=-q^5, f)^5/subs(q=-q, f), where f = A010815 = Sum_{k=-infinity, infinity} (-1)^k*q^(k*(3*k-1)/2).
EXAMPLE
G.f. = 1 + 10*q - 30*q^4 + 30*q^5 - 20*q^6 + 70*q^9 - 20*q^10 + 120*q^11 - 60*q^14 + ...
MATHEMATICA
f[q_] := Sum[(-1)^k*q^(k*(3*k - 1)/2), {k, - Infinity, Infinity}];
CoefficientList[Series[f[-q]^5/f[-q^5] + 5*q*f[-q^5]^5/f[-q], {q, 0, 70}], q] (* G. C. Greubel, May 29 2019 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Oct 06 2001
STATUS
approved