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%I #9 Mar 12 2021 22:24:47
%S 1,3,2,1,5,5,3,5,4,4,6,6,3,5,9,6,10,4,3,13,4,5,9,8,5,8,12,4,13,10,7,
%T 14,5,5,11,8,9,12,6,7,15,15,6,13,12,6,13,6,7,21,17,6,13,8,10,12,14,9,
%U 8,15,6,22,8,9,22,14,10,11,15,11,22,16,6,8,14,11
%N Expansion of phi(x) * psi(x) * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A246837/b246837.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of q^(-5/8) * eta(q^2)^7 * eta(q^8)^2 / (eta(q)^3 * eta(q^4)^3) in powers of q.
%F Euler transform of period 8 sequence [3, -4, 3, -1, 3, -4, 3, -3, ...].
%e G.f. = 1 + 3*x + 2*x^2 + x^3 + 5*x^4 + 5*x^5 + 3*x^6 + 5*x^7 + 4*x^8 + ...
%e G.f. = q^5 + 3*q^13 + 2*q^21 + q^29 + 5*q^37 + 5*q^45 + 3*q^53 + 5*q^61 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(-5/8)* eta[q^2]^7*eta[q^8]^2/(eta[q]^3*eta[q^4]^3), {q,0,60}], q]]; Table[ a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Aug 05 2018 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 * eta(x^8 + A)^2 / (eta(x + A)^3 * eta(x^4 + A)^3), n))};
%K nonn
%O 0,2
%A _Michael Somos_, Sep 04 2014
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