A202204 - OEIS

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

%S 1,1,-2,1,-3,6,-3,0,5,-7,-4,9,-1,-13,14,3,-1,-7,-6,19,-3,-13,-9,4,24,

%T -6,-20,8,-6,18,7,7,-27,-30,41,1,15,-9,-35,1,-9,39,18,-21,12,-25,-24,

%U -8,49,41,5,-51,-37,1,-18,61,8,16,3,-33,-40,-49,52,26,14,53,32

%N G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1-x^k)^3.

%C Compare g.f. to: (1 - eta(x))/x = Sum_{n>=0} x^n*Product_{k=1..n} (1-x^k) = 1 + x - x^4 - x^6 + x^11 + x^14 - x^21 - x^25 + x^34 + x^39 +..., where eta(q) is the Dedekind eta function without the q^(1/24) factor.

%H Paul D. Hanna, <a href="/A202204/b202204.txt">Table of n, a(n) for n = 0..1001</a>

%e G.f.: A(x) = 1 + x - 2*x^2 + x^3 - 3*x^4 + 6*x^5 - 3*x^6 + 5*x^8 - 7*x^9 +...

%e where A(x) = 1 + x*(1-x)^3 + x^2*(1-x)^3*(1-x^2)^3 + x^3*(1-x)^3*(1-x^2)^3*(1-x^3)^3 +...

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

%Y Cf. A202205.

%K sign

%O 0,3

%A _Paul D. Hanna_, Dec 14 2011