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%I #21 Jun 18 2019 03:19:55
%S 1,0,-1,-1,-1,-1,0,0,1,1,2,2,2,2,2,1,1,0,-1,-2,-2,-4,-4,-5,-5,-6,-5,
%T -6,-4,-4,-3,-2,1,1,4,5,8,9,12,12,15,15,17,16,18,15,16,13,13,8,7,1,0,
%U -7,-9,-17,-19,-27,-29,-37,-38,-46,-46,-53,-51,-57,-53,-57,-51,-53,-45,-45,-32,-31
%N G.f.: Sum_{n>=0} (-1)^n* x^(n*(n+1)) / Product_{k=1..n} (1-x^k).
%C Conjecture: a(n+1) = A286744(n) - A286745(n). - _George Beck_ May 13 2017
%H Alois P. Heinz, <a href="/A224898/b224898.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from Paul D. Hanna)
%e G.f.: A(x) = 1 - x^2 - x^3 - x^4 - x^5 + x^8 + x^9 + 2*x^10 + 2*x^11 + 2*x^12 + 2*x^13 + 2*x^14 + x^15 + x^16 - x^18 +...
%e where
%e A(x) = 1 - x^2/(1-x) + x^6/((1-x)*(1-x^2)) - x^12/((1-x)*(1-x^2)*(1-x^3)) + x^20/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) - x^30/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)) +...
%o (PARI) a(n)=polcoeff(sum(m=0, sqrtint(n), (-1)^m*x^(m*(m+1))/prod(k=1, m, 1-x^k,1+x*O(x^n))),n)
%o for(n=0, 80, print1(a(n), ", "))
%Y Cf. A227620, A227543, A039924, A005169, A286744, A286745, A003106.
%K sign,look
%O 0,11
%A _Paul D. Hanna_, Jul 24 2013
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