A230280 Expansion of q^(-1/3) * eta(q)^4 * eta(q^2)^2 in powers of q.

1, -4, 0, 16, -10, -16, 0, 0, 39, 0, 0, -32, -70, 64, 0, 0, 49, 40, 0, -80, -22, -64, 0, 0, 110, 0, 0, 160, -128, 0, 0, 0, -130, -156, 0, 112, 182, 0, 0, 0, 121, 0, 0, -160, 0, -128, 0, 0, -320, 280, 0, 0, 170, 256, 0, 0, -69, 0, 0, -320, 38, 0, 0, 0, -190

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 psi(x) * f(-x)^5 = phi(-x)^2 * f(-x^2)^4 in powers of x where phi(), psi(), f() are Ramanujan theta functions.

Euler transform of period 2 sequence [ -4, -6, ...].

G.f.: Product_{k>0} (1 - x^k)^4 * (1 - x^(2*k))^2.

a(4*n + 2) = a(8*n + 7) = 0. a(n) = A230277(3*n + 1).

Example

G.f. = 1 - 4*x + 16*x^3 - 10*x^4 - 16*x^5 + 39*x^8 - 32*x^11 + ...
G.f. = q - 4*q^4 + 16*q^10 - 10*q^13 - 16*q^16 + 39*q^25 - 32*q^34 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x]^4 QPochhammer[ x^2]^2, {x, 0, n}];

Prog

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

Crossrefs

Cf. A230277.

Sequence in context: A208451 A207541 A158802 * A030212 A167359 A259491

Adjacent sequences: A230277 A230278 A230279 * A230281 A230282 A230283

Keyword

sign

Author

Michael Somos, Oct 15 2013

Status

approved