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%I #9 Mar 12 2021 22:24:47
%S 1,1,0,1,1,1,0,0,2,1,1,1,0,0,1,0,1,1,1,2,0,1,0,1,1,1,1,0,0,0,2,1,0,1,
%T 1,1,1,0,1,1,1,0,1,1,0,1,2,0,0,1,1,2,0,1,0,0,1,0,1,1,0,1,0,2,1,2,1,0,
%U 2,0,1,1,0,0,2,0,0,0,1,1,0,0,0,1,2,3,1
%N Expansion of psi(x^3) * f(x, x^5) in powers of x where psi(), f() 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="/A255319/b255319.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 chi(x) * f(-x^6) * f(-x^12) in powers of x where chi(), f() are Ramanujan theta functions.
%F Expansion of q^(-17/24) * eta(q^2)^2 * eta(q^6) * eta(q^12) / (eta(q) * eta(q^4)) in powers of q.
%F Euler transform of period 12 sequence [ 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, -2, ...].
%e G.f. = 1 + x + x^3 + x^4 + x^5 + 2*x^8 + x^9 + x^10 + x^11 + x^14 + x^16 + ...
%e G.f. = q^17 + q^41 + q^89 + q^113 + q^137 + 2*q^209 + q^233 + q^257 + q^281 + ...
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x^6] QPochhammer[ x^12] QPochhammer[ -x, x^2], {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^6 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^4 + A)), n))};
%K nonn
%O 0,9
%A _Michael Somos_, Feb 21 2015
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