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A268298 G.f.: Sum_{n=-oo..+oo} x^n * (1 - x^n)^(3*n).

%I A268298 #9 Mar 29 2016 18:31:26
%S A268298 1,1,-3,1,-12,-9,-8,-20,-59,1,-43,-54,-101,-77,-89,127,-307,-135,-26,
%T A268298 -170,73,85,199,-252,-888,1066,924,1,1177,-405,2970,-464,1009,-164,
%U A268298 5577,10396,-2978,-665,10869,-1286,14576,-819,15499,-902,19934,17551,32546,-1080,-51905,53089,74231,-24309,55317,-1377,-80,42439,103857,-75581,117016,-1710
%N A268298 G.f.: Sum_{n=-oo..+oo} x^n * (1 - x^n)^(3*n).
%C A268298 Compare to the identity: Sum_{n=-oo..+oo} x^n * (1 - x^n)^n = 0.
%H A268298 Paul D. Hanna, <a href="/A268298/b268298.txt">Table of n, a(n) for n = 0..2200</a>
%F A268298 G.f.: Sum_{n=-oo..+oo} (-1)^n * x^(3*n^2-n) / (1 - x^n)^(3*n).
%F A268298 For n>0, a(n) = 1 iff n = 3^k for k>=0 (conjecture).
%e A268298 G.f.: A(x) = 1 + x - 3*x^2 + x^3 - 12*x^4 - 9*x^5 - 8*x^6 - 20*x^7 - 59*x^8 + x^9 - 43*x^10 - 54*x^11 - 101*x^12 - 77*x^13 - 89*x^14 + 127*x^15 +...
%o A268298 (PARI) {a(n) = local(A=1); A = sum(k=-n-1, n+1, x^k*(1-x^k + x*O(x^n) )^(3*k) ); polcoeff(A, n)}
%o A268298 for(n=0, 60, print1(a(n), ", "))
%Y A268298 Cf. A260147.
%K A268298 sign
%O A268298 0,3
%A A268298 _Paul D. Hanna_, Mar 29 2016