A262156 Expansion of f(-x^6)^3 / (f(x)^2 * psi(x)) in powers of x where psi(), f() are Ramanujan theta functions.

1, -3, 8, -19, 42, -86, 166, -309, 557, -974, 1661, -2773, 4543, -7316, 11600, -18140, 28011, -42751, 64550, -96503, 142951, -209939, 305844, -442213, 634865, -905361, 1282957, -1807175, 2531156, -3526051, 4886764, -6739401, 9250902, -12641475, 17200638

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^(-13/24) * eta(q)^3 * eta(q^4)^2 * eta(q^6)^3 / eta(q^2)^8 in powers of q.

Euler transform of period 12 sequence [-3, 5, -3, 3, -3, 2, -3, 3, -3, 5, -3, 0, ...].

Example

G.f. = 1 - 3*x + 8*x^2 - 19*x^3 + 42*x^4 - 86*x^5 + 166*x^6 + ...
G.f. = q^13 - 3*q^37 + 8*q^61 - 19*q^85 + 42*q^109 - 86*q^133 + ...

Mathematica

a[ n_] := SeriesCoefficient[ 2 x^(1/8) QPochhammer[ x^6]^3 / (QPochhammer[ -x]^2 EllipticTheta[ 2 , 0, x^(1/2)]), {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^4 + A)^2 * eta(x^6 + A)^3 / eta(x^2 + A)^8, n))};
(PARI) q='q+O('q^99); Vec(eta(q)^3*eta(q^4)^2*eta(q^6)^3/eta(q^2)^8) \\ Altug Alkan, Jul 31 2018

Crossrefs

Sequence in context: A072916 A298406 A074839 * A002318 A229198 A095681

Adjacent sequences: A262153 A262154 A262155 * A262157 A262158 A262159

Keyword

sign

Author

Michael Somos, Sep 13 2015

Status

approved