A232166 Expansion of phi(x) / psi(x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.

1, 2, -2, -4, 5, 6, -10, -12, 17, 24, -30, -40, 50, 62, -80, -100, 127, 160, -196, -244, 296, 360, -442, -532, 649, 786, -940, -1132, 1347, 1600, -1910, -2260, 2682, 3176, -3734, -4400, 5157, 6032, -7066, -8240, 9616, 11202, -13002, -15096, 17469, 20192

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

Euler transform of period 4 sequence [ 2, -5, 2, 1, ...].

Example

G.f. = 1 + 2*x - 2*x^2 - 4*x^3 + 5*x^4 + 6*x^5 - 10*x^6 - 12*x^7 + ...
G.f. = 1/q + 2*q - 2*q^3 - 4*q^5 + 5*q^7 + 6*q^9 - 10*q^11 -12*q^13 + ...

Mathematica

a[ n_]:= SeriesCoefficient[4*x^(1/2)*EllipticTheta[3, 0, x]/EllipticTheta[ 2, 0, x]^2, {x, 0, n}];
a[ n_]:= SeriesCoefficient[QPochhammer[x^2]^7/(QPochhammer[x]^2* QPochhammer[x^4]^6), {x, 0, n}];

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 / (eta(x + A)^2 * eta(x^4 + A)^6), n))};

Crossrefs

Sequence in context: A250114 A056219 A085140 * A325555 A138883 A257632

Adjacent sequences: A232163 A232164 A232165 * A232167 A232168 A232169

Keyword

sign

Author

Michael Somos, Nov 19 2013

Status

approved