A260167 Expansion of psi(x^4) * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions.

1, 2, 3, 3, 4, 7, 7, 8, 7, 10, 11, 10, 13, 11, 15, 16, 19, 18, 14, 20, 21, 20, 21, 21, 25, 22, 27, 31, 23, 30, 31, 35, 28, 27, 35, 36, 37, 38, 32, 34, 41, 39, 43, 35, 49, 46, 43, 48, 42, 55, 51, 49, 50, 38, 55, 52, 57, 63, 47, 60, 54, 62, 63, 51, 65, 66, 67

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^(-23/24) * eta(q^2)^2 * eta(q^3)^3 * eta(q^8)^2 / (eta(q)^2 * eta(q^4)) in powers of q.

Euler transform of period 24 sequence [ 2, 0, -1, 1, 2, -3, 2, -1, -1, 0, 2, -2, 2, 0, -1, -1, 2, -3, 2, 1, -1, 0, 2, -4, ...].

6 * a(n) = A260158(4*n + 3).

Example

G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 4*x^4 + 7*x^5 + 7*x^6 + 8*x^7 + 7*x^8 + ...
G.f. = q^23 + 2*q^47 + 3*q^71 + 3*q^95 + 4*q^119 + 7*q^143 + 7*q^167 + ...

Mathematica

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

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^8 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)), n))};

Crossrefs

Cf. A260158.

Sequence in context: A119795 A207618 A119614 * A035540 A114863 A152980

Adjacent sequences: A260164 A260165 A260166 * A260168 A260169 A260170

Keyword

nonn

Author

Michael Somos, Nov 09 2015

Status

approved