OFFSET
0,4
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..5000
FORMULA
G.f.: ( Product_{n>=1} 1 - x^n )^2 / (1-x)^3.
EXAMPLE
G.f.: A(x) = 1 + x - x^2 - 3*x^3 - 4*x^4 - 2*x^5 + x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 6*x^10 + 2*x^11 - 4*x^12 - 10*x^13 - 13*x^14 - 15*x^15 +...
where
log(A(x)) = x*(1-3*x)/(1-x) + x^2/2*(1-3*x^2)/(1-x^2) + x^3/3*(1-3*x^3)/(1-x^3) + x^4/4*(1-3*x^4)/(1-x^4) + x^5/5*(1-3*x^5)/(1-x^5) +...
Also,
A(x)*(1-x)^3 = (1-x)^2 * (1-x^2)^2 * (1-x^3)^2 * (1-x^4)^2 * (1-x^5)^3 *...
PROG
(PARI) {a(n) = my(A=1); A = exp( sum(k=1, n+1, (x^k*(1 - 3*x^k)/(1 - x^k)) /k +x*O(x^n) ) ); polcoeff(A, n)}
for(n=0, 120, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign,look
AUTHOR
Paul D. Hanna, Dec 14 2015
STATUS
approved