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A257402 Expansion of chi(x) * psi(-x^3) * psi(x^12) in powers of x where psi(), chi() are Ramanujan theta functions.

%I A257402 #9 Feb 16 2025 08:33:25
%S A257402 1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,2,
%T A257402 0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,2,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,
%U A257402 1,1,0,0,1,1,0,0,1,2,0,0,1,0,0,0,0,1,0
%N A257402 Expansion of chi(x) * psi(-x^3) * psi(x^12) in powers of x where psi(), chi() are Ramanujan theta functions.
%C A257402 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A257402 G. C. Greubel, <a href="/A257402/b257402.txt">Table of n, a(n) for n = 0..1000</a>
%H A257402 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A257402 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A257402 Expansion of q^(-11/6) * eta(q^2)^2 * eta(q^3) * eta(q^24)^2 / (eta(q) * eta(q^4) * eta(q^6)) in powers of q.
%F A257402 a(4*n) = A255318(n). a(4*n + 1) = A255319(n). a(4*n + 2) = a(4*n + 3) = 0.
%e A257402 G.f. = 1 + x + x^5 + x^8 + x^12 + x^13 + x^16 + x^17 + x^20 + x^21 + x^28 + ...
%e A257402 G.f. = q^11 + q^17 + q^41 + q^59 + q^83 + q^89 + q^107 + q^113 + q^131 + ...
%t A257402 a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2] EllipticTheta[ 2, 0, x^6] EllipticTheta[ 2, Pi/4, x^(3/2)] / (2^(3/2) x^(15/8)), {x, 0, n}];
%o A257402 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^24 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)), n))};
%Y A257402 Cf. A255318, A255319.
%K A257402 nonn
%O A257402 0,34
%A A257402 _Michael Somos_, Apr 21 2015