A227033 Expansion of (phi(x) / f(-x^4))^2 in powers of x where phi(), f() are Ramanujan theta functions.

1, 4, 4, 0, 6, 16, 8, 0, 17, 40, 28, 0, 38, 96, 56, 0, 84, 204, 124, 0, 172, 400, 232, 0, 325, 760, 448, 0, 594, 1376, 784, 0, 1049, 2404, 1388, 0, 1796, 4096, 2320, 0, 3005, 6808, 3864, 0, 4912, 11072, 6216, 0, 7877, 17688, 9940, 0, 12430, 27792, 15488, 0

Offset

0,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500 (terms 0..55 from Michael Somos)

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(1/3) * (eta(q^2)^5 / (eta(q)^2 * eta(q^4)^3))^2 in powers of q.

Euler transform of period 4 sequence [4, -6, 4, 0, ...].

a(4*n + 3) = 0. a(2*n) = A112160(n). a(4*n + 1) = 4 * A022569(n).

Example

G.f. = 1 + 4*x + 4*x^2 + 6*x^4 + 16*x^5 + 8*x^6 + 17*x^8 + 40*x^9 + 28*x^10 + ...
G.f. = 1/q + 4*q^2 + 4*q^5 + 6*q^11 + 16*q^14 + 8*q^17 + 17*q^23 + 40*q^26 + ...

Mathematica

a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, x] / QPochhammer[ x^4])^2, {x, 0, n}];

Prog

(PARI) {a(n) = my(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))^2, n))};

Crossrefs

Cf. A022569, A112160.

Sequence in context: A169783 A133657 A121455 * A285050 A262949 A200519

Adjacent sequences: A227030 A227031 A227032 * A227034 A227035 A227036

Keyword

nonn

Author

Michael Somos, Jul 03 2013

Status

approved