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A196345 The 5th power of the g.f. equals the g.f. of A196344.

%I A196345 #14 Mar 13 2015 22:55:40
%S A196345 1,1,-2,6,-21,80,-320,1326,-5637,24434,-107542,479196,-2157045,
%T A196345 9792702,-44780606,206055345,-953305628,4431463845,-20686696836,
%U A196345 96931500441,-455722376856,2149086834269,-10162544424168,48176923110789,-228913128188293,1089973053510359
%N A196345 The 5th power of the g.f. equals the g.f. of A196344.
%C A196345 A196344 is defined as the coefficients in the g.f. Q(x), where -2 <= A196344(n) <= 2 for all n>1 with initial terms {1,5}, such that Q(x)^(1/5) consists entirely of integer coefficients.
%C A196345 Limit a(n+1)/a(n) = -5.0015989761 6639938823 4051883169 0463138590 3476719792 3351242105 ...
%H A196345 Paul D. Hanna, <a href="/A196345/b196345.txt">Table of n, a(n) for n = 0..200</a>
%e A196345 G.f.: A(x) = 1 + x - 2*x^2 + 6*x^3 - 21*x^4 + 80*x^5 - 320*x^6 + 1326*x^7 - 5637*x^8 + 24434*x^9 - 107542*x^10 +...
%e A196345 where
%e A196345 A(x)^5 = 1 + 5*x + x^5 - 2*x^10 + x^15 - x^20 + x^35 - 2*x^40 - x^45 - 2*x^50 + x^55 + 2*x^65 - x^70 + 2*x^80 +...+ A196344(n)*x^n +...
%e A196345 A196344 begins: [1,5,0,0,0,1,0,0,0,0,-2,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,...].
%o A196345 (PARI) {a(n)=local(A=1+5*x); if(n==0, 1, for(j=1, n, for(k=-2, 2, t=polcoeff((A+k*x^j+x*O(x^j))^(1/5), j);
%o A196345 if(denominator(t)==1, A=A+k*x^j; break))); polcoeff((A+x*O(x^n))^(1/5), n))}
%Y A196345 Cf. A196344, A196346, A106223.
%K A196345 sign
%O A196345 0,3
%A A196345 _Paul D. Hanna_, Oct 01 2011