A064512 - OEIS

%I #9 May 30 2019 00:50:48

%S 1,14,42,-14,-70,-42,70,-140,42,126,210,-84,294,-294,-84,0,154,-504,

%T 378,-630,882,-350,-252,252,1190,350,1470,-1148,1372,-756,0,-1680,

%U -630,-1708,2520,-1050,-630,-532,3150,0,3570,-2940,1750,812,420,-3066,756,-3864

%N Ramanujan's function F_7(q).

%H G. C. Greubel, <a href="/A064512/b064512.txt">Table of n, a(n) for n = 0..5000</a>

%H S. Ahlgren, <a href="http://dx.doi.org/10.1090/S0002-9939-99-05181-3">The sixth, eighth, ninth and tenth powers of Ramanujan's theta function</a>, Proc. Amer. Math. Soc., 128 (1999), 1333-1338; F_7(q).

%F 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).

%e 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 + ...

%t f[q_]:= Sum[(-1)^k*q^(k*(3*k-1)/2), {k, -Infinity, Infinity}];

%t 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 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_, Oct 06 2001