A227175 Expansion of (phi(x) / f(-x^4))^4 in powers of x where phi(), f() are Ramanujan theta functions.

1, 8, 24, 32, 28, 80, 192, 192, 134, 408, 864, 800, 568, 1520, 3072, 2752, 1809, 4808, 9456, 8192, 5316, 13616, 26112, 22144, 13990, 35376, 66624, 55584, 34696, 86016, 159744, 131392, 80724, 198256, 363720, 295776, 180068, 436816, 793344, 638976, 384940

Offset: 0

Author

Michael Somos, Jul 03 2013

Keywords

• nonn

Comments

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

Examples

			1 + 8*x + 24*x^2 + 32*x^3 + 28*x^4 + 80*x^5 + 192*x^6 + 192*x^7 + 134*x^8 + ...
q^-2 + 8*q + 24*q^4 + 32*q^7 + 28*q^10 + 80*q^13 + 192*q^16 + 192*q^19 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Michael Somos, Introduction to Ramanujan theta functions
• Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Crossrefs

Cf. A022569, A227033.

Programs

Mathematica

a[ n_]:= SeriesCoefficient[(EllipticTheta[3,0,q]/QPochhammer[q^4])^4, {q, 0, n}];

PARI

{a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 / (eta(x + A)^2 * eta(x^4 + A)^3))^4, n))}

Formula

Expansion of q^(2/3) * (eta(q^2)^5 / (eta(q)^2 * eta(q^4)^3))^4 in powers of q.

Euler transform of period 4 sequence [ 8, -12, 8, 0, ...].

a(2*n + 1) = 8 * A022569(n). Convolution square of A227033.