A228831 Expansion of psi(x)^2 * phi(-x^2)^4 in powers of x where phi(), psi() are Ramanujan theta functions.

1, 2, -7, -14, 18, 32, -21, -14, 16, -30, -14, -14, -15, 66, 48, 82, -28, -160, 66, -32, -95, 36, -30, 128, -14, -94, 64, 18, 98, 98, 105, -92, -112, -96, -206, -64, -28, 226, -126, -46, 320, 32, 27, -142, 208, -30, -60, 64, -206, 322, -16, -28, -48, -224

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 f(x)^4 * f(-x)^2 in powers of x where f() is a Ramanujan theta function.

Expansion of q^(-1/4) * (eta(q^2)^6 / (eta(q) * eta(q^4)^2))^2 in powers of q.

Euler transform of period 4 sequence [2, -10, 2, -6, ...].

G.f.: (Product_{k>0} (1 - x^(2*k))^3 * (1 + x^k) / (1 + x^(2*k))^2)^2.

Example

G.f. = 1 + 2*x - 7*x^2 - 14*x^3 + 18*x^4 + 32*x^5 - 21*x^6 - 14*x^7 + 16*x^8 + ...
G.f. = q + 2*q^5 - 7*q^9 - 14*q^13 + 18*q^17 + 32*q^21 - 21*q^25 - 14*q^29 + ...

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A319250 A018349 A256798 * A285682 A018363 A187142

Adjacent sequences: A228828 A228829 A228830 * A228832 A228833 A228834

Keyword

sign

Author

Michael Somos, Sep 04 2013

Status

approved