cp's OEIS Frontend

A261394 Expansion of phi(q)^4 / phi(q^3) in powers of q where phi() is a Ramanujan theta function.

%I A261394 #13 Feb 16 2025 08:33:26
%S A261394 1,8,24,30,8,0,36,48,24,32,48,48,30,0,48,72,8,48,96,48,0,0,96,96,36,
%T A261394 56,48,102,48,0,120,48,24,72,48,96,32,0,96,120,48,48,144,144,48,0,96,
%U A261394 96,30,56,120,144,0,0,108,96,48,120,144,48,72,0,144,192,8,96
%N A261394 Expansion of phi(q)^4 / phi(q^3) in powers of q where phi() is a Ramanujan theta function.
%C A261394 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A261394 G. C. Greubel, <a href="/A261394/b261394.txt">Table of n, a(n) for n = 0..2500</a>
%H A261394 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A261394 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A261394 Euler transform of period 12 sequence [ 8, -12, 6, -4, 8, -9, 8, -4, 6, -12, 8, -3, ...].
%F A261394 a(n) = A004013(12*n).
%e A261394 G.f. = 1 + 8*x + 24*x^2 + 30*x^3 + 8*x^4 + 36*x^6 + 48*x^7 + 24*x^8 + ...
%t A261394 a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q]^4 / EllipticTheta[ 3, 0, q^3], {q, 0, n}];
%o A261394 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^20 * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A)^8 * eta(x^4 + A)^8 * eta(x^6 + A)^5), n))};
%Y A261394 Cf. A004013.
%K A261394 nonn
%O A261394 0,2
%A A261394 _Michael Somos_, Aug 17 2015