A164270 Expansion of f(x^3)^3 * phi(x^3) / (f(x) * phi(x)^3) in powers of x where f(), phi() are Ramanujan theta functions.

1, -7, 32, -114, 350, -967, 2468, -5916, 13471, -29384, 61784, -125838, 249230, -481506, 909788, -1684824, 3063657, -5478698, 9648360, -16752522, 28708214, -48599047, 81338660, -134687856, 220802690, -358574468, 577143752, -921144678, 1458485460

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^(-1/3) * eta(q)^7 * eta(q^4)^7 * eta(q^6)^14 / (eta(q^2)^18 * eta(q^3)^5 * eta(q^12)^5) in powers of q.

Euler transform of period 12 sequence [ -7, 11, -2, 4, -7, 2, -7, 4, -2, 11, -7, 0, ...].

a(n) = A164269(3*n + 1).

Example

G.f. = 1 - 7*x + 32*x^2 - 114*x^3 + 350*x^4 - 967*x^5 + 2468*x^6 + ...
G.f. = q - 7*q^4 + 32*q^7 - 114*q^10 + 350*q^13 - 967*q^16 + 2468*q^19 + ...

Mathematica

f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A164270[n_] := SeriesCoefficient[(f[q^3, -q^6]^3*f[q^3, q^3])/( (f[q, -q^2])*f[q, q]^3), {q, 0, n}]; Table[A164270[n], {n, 0, 50}] (* G. C. Greubel, Sep 16 2017 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^7 * eta(x^4 + A)^7 * eta(x^6 + A)^14 / (eta(x^2 + A)^18 * eta(x^3 + A)^5 * eta(x^12 + A)^5), n))};

Crossrefs

Cf. A164269.

Sequence in context: A190096 A254407 A219510 * A182820 A001794 A140289

Adjacent sequences: A164267 A164268 A164269 * A164271 A164272 A164273

Keyword

sign

Author

Michael Somos, Aug 11 2009

Status

approved