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A246650 Expansion of phi(x) * chi(-x) * psi(x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.

%I A246650 #11 Jul 23 2025 11:31:52
%S A246650 1,1,-2,0,2,-3,-2,0,1,2,-2,0,2,0,-2,0,3,2,0,0,2,-3,-2,0,2,2,-2,0,0,0,
%T A246650 -4,0,2,1,-2,0,2,-6,0,0,1,2,-2,0,4,0,-2,0,0,2,-2,0,2,0,-2,0,3,2,-2,0,
%U A246650 2,0,0,0,2,3,-2,0,0,-6,-2,0,4,0,-2,0,2,0,0,0
%N A246650 Expansion of phi(x) * chi(-x) * psi(x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
%C A246650 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A246650 G. C. Greubel, <a href="/A246650/b246650.txt">Table of n, a(n) for n = 0..1000</a>
%H A246650 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A246650 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A246650 Expansion of q^(-1/3) * eta(q^2)^4 * eta(q^6)^2 / (eta(q) * eta(q^3) * eta(q^4)^2) in powers of q.
%F A246650 a(2*n) = A129451(n). a(4*n) = A123884(n). a(4*n + 1) = A122861(n). a(4*n + 2) = -2 * A121361(n). a(4*n + 3) = 0.
%F A246650 a(8*n) = A131961(n). a(8*n + 1) = A097195(n). a(8*n + 2) = -2 * A131962(n). a(8*n + 4) = 2 * A131963(n). a(8*n + 6) = -2 * A131964(n).
%F A246650 a(16*n + 1) = A123884(n). a(16*n + 5) = -3 * A033687(n). a(16*n + 9) = 2 * A121361(n). a(16*n + 13) = 0.
%e A246650 G.f. = 1 + x - 2*x^2 + 2*x^4 - 3*x^5 - 2*x^6 + x^8 + 2*x^9 - 2*x^10 + ...
%e A246650 G.f. = q + q^4 - 2*q^7 + 2*q^13 - 3*q^16 - 2*q^19 + q^25 + 2*q^28 - ...
%o A246650 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^6 + A)^2 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A)^2), n))};
%Y A246650 Cf. A033687, A121361, A122861, A123884, A129451, A131961, A131962, A131963, A131964.
%K A246650 sign
%O A246650 0,3
%A A246650 _Michael Somos_, Aug 31 2014