A261394 - OEIS

%I #12 Mar 12 2021 22:24:48

%S 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 56,48,102,48,0,120,48,24,72,48,96,32,0,96,120,48,48,144,144,48,0,96,

%U 96,30,56,120,144,0,0,108,96,48,120,144,48,72,0,144,192,8,96

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

%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

%H G. C. Greubel, <a href="/A261394/b261394.txt">Table of n, a(n) for n = 0..2500</a>

%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>

%F Euler transform of period 12 sequence [ 8, -12, 6, -4, 8, -9, 8, -4, 6, -12, 8, -3, ...].

%F a(n) = A004013(12*n).

%e G.f. = 1 + 8*x + 24*x^2 + 30*x^3 + 8*x^4 + 36*x^6 + 48*x^7 + 24*x^8 + ...

%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q]^4 / EllipticTheta[ 3, 0, q^3], {q, 0, n}];

%o (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 Cf. A004013.

%K nonn

%O 0,2

%A _Michael Somos_, Aug 17 2015