A260166 Expansion of phi(x^2) * f(-x^3)^3 / chi(-x)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions.

1, 2, 5, 7, 9, 11, 10, 15, 14, 19, 21, 21, 28, 24, 29, 26, 26, 35, 37, 39, 41, 34, 43, 47, 49, 56, 42, 55, 57, 50, 56, 50, 60, 74, 69, 76, 52, 70, 84, 79, 81, 66, 85, 74, 98, 91, 74, 88, 97, 99, 86, 84, 105, 107, 109, 122, 90, 98, 124, 119, 121, 105, 125, 127

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^(-11/24) * eta(q^3)^3 * eta(q^4)^5 / (eta(q)^2 * eta(q^8)^2) in powers of q.

Euler transform of period 24 sequence [ 2, 2, -1, -3, 2, -1, 2, -1, -1, 2, 2, -6, 2, 2, -1, -1, 2, -1, 2, -3, -1, 2, 2, -4, ...].

3 * a(n) = A260158(4*n + 1).

Example

G.f. = 1 + 2*x + 5*x^2 + 7*x^3 + 9*x^4 + 11*x^5 + 10*x^6 + 15*x^7 + 14*x^8 + ...
G.f. = q^11 + 2*q^35 + 5*q^59 + 7*q^83 + 9*q^107 + 11*q^131 + 10*q^155 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 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^3 + A)^3 * eta(x^4 + A)^5 / (eta(x + A)^2 * eta(x^8 + A)^2), n))};

Crossrefs

Cf. A260158.

Sequence in context: A174272 A062288 A077059 * A007300 A256699 A247421

Adjacent sequences: A260163 A260164 A260165 * A260167 A260168 A260169

Keyword

nonn,changed

Author

Michael Somos, Nov 09 2015

Status

approved