cp's OEIS Frontend

A224831 Expansion of phi(-x^3)^2 * psi(x) / chi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions.

%I A224831 #13 Feb 16 2025 08:33:19
%S A224831 1,3,5,6,5,6,7,9,11,8,9,7,11,13,8,14,11,16,14,9,14,7,18,19,12,13,10,
%T A224831 21,19,17,21,10,15,17,17,15,14,26,20,13,18,22,21,26,17,20,13,20,30,9,
%U A224831 24,21,26,21,13,25,20,27,30,21,17,20,35,28,18,22,16,29,25
%N A224831 Expansion of phi(-x^3)^2 * psi(x) / chi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
%C A224831 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A224831 G. C. Greubel, <a href="/A224831/b224831.txt">Table of n, a(n) for n = 0..1000</a>
%H A224831 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A224831 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A224831 Expansion of q^(-5/24) * eta(q^2)^4 * eta(q^3)^4 / (eta(q)^3 * eta(q^6)^2) in powers of q.
%F A224831 Euler transform of period 6 sequence [ 3, -1, -1, -1, 3, -3, ...].
%F A224831 a(n) = A224823(3*n).
%e A224831 1 + 3*x + 5*x^2 + 6*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 9*x^7 + 11*x^8 + 8*x^9 + ...
%e A224831 q^5 + 3*q^29 + 5*q^53 + 6*q^77 + 5*q^101 + 6*q^125 + 7*q^149 + 9*q^173 + ...
%t A224831 a[n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^3]^2 EllipticTheta[ 2, 0, q^(1/2)]/(2 q^(1/8) QPochhammer[q, q^2]^2), {q, 0, n}]
%o A224831 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^3 + A)^4 / (eta(x + A)^3 * eta(x^6 + A)^2), n))}
%Y A224831 Cf. A224823.
%K A224831 nonn
%O A224831 0,2
%A A224831 _Michael Somos_, Jul 21 2013