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A255318 Expansion of psi(x^3) * f(x^2, x^4) in powers of x where psi(), f() are Ramanujan theta functions.

%I A255318 #12 Feb 16 2025 08:33:25
%S A255318 1,0,1,1,1,1,0,1,0,1,1,1,0,2,1,0,0,1,1,1,1,0,1,1,1,0,0,1,1,0,2,0,2,2,
%T A255318 1,0,0,0,0,1,1,0,1,0,2,1,0,2,1,1,0,0,1,1,1,2,0,0,0,1,1,1,1,1,0,1,0,1,
%U A255318 0,1,2,0,0,2,1,1,0,1,0,1,1,0,1,1,1,0,1
%N A255318 Expansion of psi(x^3) * f(x^2, x^4) in powers of x where psi(), f() are Ramanujan theta functions.
%C A255318 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A255318 G. C. Greubel, <a href="/A255318/b255318.txt">Table of n, a(n) for n = 0..1000</a>
%H A255318 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A255318 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A255318 Expansion of f(x^3) * f(-x^6) / chi(-x^2) in powers of x where chi(), f() are Ramanujan theta functions.
%F A255318 Expansion of q^(-11/24) * eta(q^4) * eta(q^6)^4 / (eta(q^2) * eta(q^3) * eta(q^12)) in powers of q.
%F A255318 Euler transform of period 12 sequence [ 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, -2, ...].
%e A255318 G.f. = 1 + x^2 + x^3 + x^4 + x^5 + x^7 + x^9 + x^10 + x^11 + 2*x^13 + ...
%e A255318 G.f. = q^11 + q^59 + q^83 + q^107 + q^131 + q^179 + q^227 + q^251 + q^275 + ...
%t A255318 a[ n_] := SeriesCoefficient[QPochhammer[-x^3]*QPochhammer[x^6]* QPochhammer[ -x^2, x^2], {x, 0, n}];
%o A255318 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^4 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)), n))};
%K A255318 nonn
%O A255318 0,14
%A A255318 _Michael Somos_, Feb 21 2015