A202145 - OEIS

%I #10 Mar 30 2012 18:37:33

%S 1,1,0,0,0,0,-1,1,0,-2,2,0,-2,2,0,-2,2,0,-1,1,0,-2,2,2,-4,2,0,-2,4,-2,

%T -2,2,0,0,0,0,-3,3,2,-4,2,0,-2,2,0,-2,2,0,0,0,-2,0,2,2,-4,2,0,-4,6,-2,

%U -1,1,0,0,-2,2,-2,2,2,-2,0,-2,0,4,-2,-2,2,0

%N G.f.: 1 + Sum_{n>=1} x^n * Product_{k=1..n} (1 - x^k) / (1 - x^(2*k+1)).

%H Paul D. Hanna, <a href="/A202145/b202145.txt">Table of n, a(n) for n = 0..500</a>

%e G.f.: A(x) = 1 + x - x^6 + x^7 - 2*x^9 + 2*x^10 - 2*x^12 + 2*x^13 - 2*x^15 +... where A(x) = 1 + x*(1-x)/(1-x^3) + x^2*(1-x)*(1-x^2)/((1-x^3)*(1-x^5)) + x^3*(1-x)*(1-x^2)*(1-x^3)/((1-x^3)*(1-x^5)*(1-x^7)) +...

%o (PARI) {a(n)=polcoeff(1 + sum(m=1,n,x^m*prod(k=1,m,(1-x^k)/(1-x^(2*k+1) +x*O(x^n)))),n)}

%Y Cf. A202146 (partial sums).

%K sign

%O 0,10

%A _Paul D. Hanna_, Dec 12 2011