A263528 Expansion of (psi(x) * psi(x^3) / f(-x^3)^2)^2 in powers of x where psi(), f() are Ramanujan theta functions.

1, 2, 1, 8, 14, 6, 38, 60, 23, 140, 208, 76, 439, 626, 221, 1232, 1704, 584, 3182, 4300, 1443, 7700, 10212, 3368, 17673, 23076, 7497, 38808, 50008, 16046, 82070, 104560, 33190, 167996, 211920, 66628, 334202, 417902, 130288, 648224, 804254, 248858, 1229148

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-1/2) * (eta(q^2)^2 * eta(q^6)^2 / (eta(q) * eta(q^3)^3))^2 in powers of q.

Euler transform of period 6 sequence [ 2, -2, 8, -2, 2, 0, ...].

-2 * a(n) = A262930(2*n + 1).

Example

G.f. = 1 + 2*x + x^2 + 8*x^3 + 14*x^4 + 6*x^5 + 38*x^6 + 60*x^7 + 23*x^8 + ...
G.f. = q + 2*q^3 + q^5 + 8*q^7 + 14*q^9 + 6*q^11 + 38*q^13 + 60*q^15 + 23*x^17 + ...

Mathematica

a[ n_] := SeriesCoefficient[ (EllipticTheta[ 2, 0, x^(1/2)] EllipticTheta[ 2, 0, x^(3/2)] / (4 QPochhammer[ x^3]^2))^2 / x, {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 * eta(x^6 + A)^2 / (eta(x + A) * eta(x^3 + A)^3))^2, n))};

Crossrefs

Cf. A262930.

Sequence in context: A151501 A102735 A088960 * A121360 A199928 A047688

Adjacent sequences: A263525 A263526 A263527 * A263529 A263530 A263531

Keyword

nonn

Author

Michael Somos, Oct 19 2015

Status

approved