OFFSET
0,5
COMMENTS
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
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 10 2015
STATUS
approved