OFFSET
0,2
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 f(-x, -x^4) * f(-x^2, +x^3) / (f(+x, -x^4) * f(-x^2, -x^3)) = f(-x, -x^9) * f(+x^3, +x^7) / (f(+x, +x^9) * f(-x^3, -x^7)) in powers of x where f(,) is the Ramanujan general theta function.
Euler transform of period 20 sequence [ -2, 1, 2, 0, 0, -1, 2, 0, -2, 0, -2, 0, 2, -1, 0, 0, 2, 1, -2, 0, ...].
a(10*n + 3) = a(10*n + 7) = 0.
EXAMPLE
G.f. = 1 - 2*x + 2*x^2 - 2*x^4 + 2*x^5 - 2*x^8 + 2*x^9 + 2*x^10 - 8*x^11 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ Product[(1 - x^k)^{ 2, -1, -2, 0, 0, 1, -2, 0, 2, 0, 2, 0, -2, 1, 0, 0, -2, -1, 2, 0}[[ Mod[k, 20, 1]]], {k, 1, n}], {x, 0, n}];
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^ [ 0, 2, -1, -2, 0, 0, 1, -2, 0, 2, 0, 2, 0, -2, 1, 0, 0, -2, -1, 2][k%20 + 1]) , n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, May 16 2015
STATUS
approved