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A255317 Expansion of psi(-x^3)^2 / chi(-x) in powers of x where psi(), chi() are Ramanujan theta functions.

%I A255317 #10 Feb 16 2025 08:33:25
%S A255317 1,1,1,0,0,1,1,2,1,0,0,1,1,1,0,1,0,0,2,1,1,1,1,1,0,1,1,0,1,0,1,0,1,1,
%T A255317 0,1,1,1,1,0,2,2,0,1,1,0,1,0,1,0,0,2,0,1,0,0,0,2,2,0,1,1,2,1,0,1,0,1,
%U A255317 0,1,1,1,1,0,0,2,2,1,0,0,0,0,1,1,0,0,1
%N A255317 Expansion of psi(-x^3)^2 / chi(-x) in powers of x where psi(), chi() are Ramanujan theta functions.
%C A255317 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A255317 G. C. Greubel, <a href="/A255317/b255317.txt">Table of n, a(n) for n = 0..1000</a>
%H A255317 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A255317 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A255317 Expansion of psi(x^6) * f(x, x^2) in powers of x where psi(), f() are Ramanujan theta functions.
%F A255317 Expansion of q^(-19/24) * eta(q^2) * eta(q^3)^2 * eta(q^12)^2 / (eta(q) * eta(q^6)^2) in powers of q.
%F A255317 Euler transform of period 12 sequence [ 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, -2, ...].
%e A255317 G.f. = 1 + x + x^2 + x^5 + x^6 + 2*x^7 + x^8 + x^11 + x^12 + x^13 + ...
%e A255317 G.f. = q^19 + q^43 + q^67 + q^139 + q^163 + 2*q^187 + q^211 + q^283 + ...
%t A255317 a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x] EllipticTheta[ 2, Pi/4, x^(3/2)]^2 / (2 x^(3/4)), {x, 0, n}];
%o A255317 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A) * eta(x^6 + A)^2), n))};
%K A255317 nonn
%O A255317 0,8
%A A255317 _Michael Somos_, Feb 21 2015