%I #19 Mar 30 2012 18:37:33

%S 1,1,1,-1,1,-1,1,3,1,-1,1,-1,1,1,1,-1,-1,1,1,1,1,-1,3,-1,1,1,1,1,-1,

%T -1,1,1,3,-1,-1,-1,1,3,3,-1,1,-1,1,1,1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,-1,

%U 3,1,1,1,1,-1,-1,-1,3,3,1,-1,-1,1,1,-1,1,-1,3

%N a(n) = A202146( 3*n*(n+1) ) for n>=0.

%C Conjecture: this sequence consists of all odd terms in A202146; the g.f. of A202146 is 1/(1-x) + Sum_{n>=1} x^n/(1-x) * Product_{k=1..n} (1 - x^k) / (1 - x^(2*k+1)), which by the conjecture has an odd coefficient of x^m iff m = 3*n*(n+1) for n>=0. The conjecture holds for at least the initial 30300 terms of A202146.

%H Paul D. Hanna, <a href="/A202150/b202150.txt">Table of n, a(n) for n = 0..100</a>

%o (PARI) {a(n)=polcoeff((1+sum(m=1,3*n*(n+1), x^m*prod(k=1, m, (1-x^k)/(1-x^(2*k+1) +x*O(x^(3*n*(n+1)))))))/(1-x+x*O(x^(3*n*(n+1)))), 3*n*(n+1))}

%Y Cf. A202146.

%K sign

%O 0,8

%A _Paul D. Hanna_, Dec 12 2011