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%I #9 May 30 2019 00:49:44
%S 1,10,0,0,-30,30,-20,0,0,70,-20,120,0,0,-60,40,-110,0,0,200,-90,120,0,
%T 0,-100,130,-120,0,0,300,-60,320,0,0,-160,120,-210,0,0,240,-100,420,0,
%U 0,-360,210,-220,0,0,430,-120,320,0,0,-200,360,-300,0,0,600,-120,620
%N Ramanujan's function F_5(q).
%H G. C. Greubel, <a href="/A064511/b064511.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_5(q).
%F 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).
%e 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 + ...
%t f[q_] := Sum[(-1)^k*q^(k*(3*k - 1)/2), {k, - Infinity, Infinity}];
%t 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 *)
%Y See A000122 for F_2, A004016 for F_3, A004013 for F_4, A064511 (this sequence) for F_5, A064512 for F_7.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Oct 06 2001
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