OFFSET
0,7
REFERENCES
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 25, Eq. (20.23).
FORMULA
Euler transform of period 4 sequence [ 0, 1, -1, 0, ...].
G.f.: 1 + Sum_{k>0} x^(k^2+k)*(1-x)(1-x^3)...(1-x^(2k-1))/((1-x^2)(1-x^4)...(1-x^(2k))).
EXAMPLE
G.f. = 1 + x^2 - x^3 + x^4 - x^5 + 2*x^6 - 2*x^7 + 2*x^8 - 3*x^9 + 4*x^10 + ...
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^((k%4==3) - (k%4==2)), 1 + x * O(x^n)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 16 2007
STATUS
approved