A262064 Expansion of f(x^9, x^15) / f(-x^2, -x^4) in powers of x where f(, ) is the Ramanujan general theta function

1, 0, 1, 0, 2, 0, 3, 0, 5, 1, 7, 1, 11, 2, 15, 4, 22, 6, 30, 9, 42, 14, 56, 20, 77, 29, 101, 41, 135, 57, 176, 78, 231, 107, 297, 143, 385, 191, 490, 253, 627, 332, 793, 432, 1003, 561, 1257, 721, 1578, 924, 1963, 1177, 2443, 1492, 3022, 1882, 3734, 2367, 4589

Offset

0,5

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

Euler transform of period 48 sequence [ 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, ...].

a(n) = A143067(2*n).

Example

G.f. = 1 + x^2 + 2*x^4 + 3*x^6 + 5*x^8 + x^9 + 7*x^10 + x^11 + 11*x^12 + ...
G.f. = q^5 + q^101 + 2*q^197 + 3*q^293 + 5*q^389 + q^437 + 7*q^485 + q^533 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^9, x^24] QPochhammer[ -x^15, x^24] QPochhammer[ x^24] / QPochhammer[ x^2], {x, 0, n}];

Prog

(PARI) {a(n) = if( n<0, 0, A = x * O(x^n); polcoeff( subst( prod(k=1, n\3, 1 - x^k * [1, 0, 0, 1, 0, 1, 0, 0][k%8 + 1], 1 + x * O(x^(n\3))), x, -x^3) / eta(x^2 + x * O(x^n)), n))};

Crossrefs

Cf. A143067.

Sequence in context: A079977 A227093 A266772 * A008799 A325346 A325836

Adjacent sequences: A262061 A262062 A262063 * A262065 A262066 A262067

Keyword

nonn

Author

Michael Somos, Sep 10 2015

Status

approved