A224831 Expansion of phi(-x^3)^2 * psi(x) / chi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions.

1, 3, 5, 6, 5, 6, 7, 9, 11, 8, 9, 7, 11, 13, 8, 14, 11, 16, 14, 9, 14, 7, 18, 19, 12, 13, 10, 21, 19, 17, 21, 10, 15, 17, 17, 15, 14, 26, 20, 13, 18, 22, 21, 26, 17, 20, 13, 20, 30, 9, 24, 21, 26, 21, 13, 25, 20, 27, 30, 21, 17, 20, 35, 28, 18, 22, 16, 29, 25

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..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-5/24) * eta(q^2)^4 * eta(q^3)^4 / (eta(q)^3 * eta(q^6)^2) in powers of q.

Euler transform of period 6 sequence [ 3, -1, -1, -1, 3, -3, ...].

a(n) = A224823(3*n).

Example

1 + 3*x + 5*x^2 + 6*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 9*x^7 + 11*x^8 + 8*x^9 + ...
q^5 + 3*q^29 + 5*q^53 + 6*q^77 + 5*q^101 + 6*q^125 + 7*q^149 + 9*q^173 + ...

Mathematica

a[n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^3]^2 EllipticTheta[ 2, 0, q^(1/2)]/(2 q^(1/8) QPochhammer[q, q^2]^2), {q, 0, n}]

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^3 + A)^4 / (eta(x + A)^3 * eta(x^6 + A)^2), n))}

Crossrefs

Cf. A224823.

Sequence in context: A161435 A354213 A343460 * A281591 A267884 A370088

Adjacent sequences: A224828 A224829 A224830 * A224832 A224833 A224834

Keyword

nonn

Author

Michael Somos, Jul 21 2013

Status

approved