OFFSET
0,2
COMMENTS
FORMULA
G.f.: A(x) = Product_{n>=1} [ 1 - (n+1)(n+2)/2*x^n + n(n+2)*x^(n+1) - n(n+1)/2*x^(n+2) ].
EXAMPLE
A(x) = (1-3x+3x^2-x^3)(1-6x^2+8x^3-3x^4)(1-10x^3+15x^4-6x^5)*...
*( 1 - (n+1)(n+2)/2*x^n + n(n+2)*x^(n+1) - n(n+1)/2*x^(n+2) )*...
Terms are divisible by 3 except at positions given by:
a(n) == 1 (mod 3) at n = [0, 45, 63, 198, 234, 459,...,9*A036498(k),..];
a(n) == -1 (mod 3) at n = [9, 18, 108, 135, 315, 360,..,9*A036499(k),..].
PROG
(PARI) {a(n)=if(n==0, 1, polcoeff(prod(k=1, n, (1-x)^3*sum(j=1, k, j*(j+1)/2*x^(j-1)) +x*O(x^n)), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Apr 10 2007
STATUS
approved