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A158120 Unsigned bisection of A157304 and A157305.

%I A158120 #3 Mar 30 2012 18:37:16
%S A158120 1,2,26,1378,141202,22716418,5218302090,1619288968386,653379470919714,
%T A158120 333014944014777730,209463165121436380282,159492000935562428176162,
%U A158120 144654795258284936534929586,154140229756873813307283828098
%N A158120 Unsigned bisection of A157304 and A157305.
%H A158120 Paul D. Hanna, <a href="/A158120/b158120.txt">Table of n, a(n) for n=0..50</a>
%e A158120 G.f.: A(x) = 1 + 2*x + 26*x^2 + 1378*x^3 + 141202*x^4 +...
%e A158120 RELATED FUNCTIONS.
%e A158120 G.f. of A157305, B(x) = x + A(-x^2), satisfies the condition
%e A158120 that both B(x) and F(x) = B(x*F(x)^2) = o.g.f. of A157307
%e A158120 have zeros for every other coefficient after initial terms:
%e A158120 A157305 = [1,1,-2,0,26,0,-1378,0,141202,0,-22716418,0,...];
%e A158120 A157307 = [1,1,0,-7,0,242,0,-17771,0,2189294,0,-404590470,0,...].
%e A158120 ...
%e A158120 G.f. of A157304, C(x) = 2+x - A(-x^2), satisfies the condition
%e A158120 that both C(x) and G(x) = C(x/G(x)^2) = o.g.f. of A157302
%e A158120 have zeros for every other coefficient after initial terms:
%e A158120 A157308 = [1,1,2,0,-26,0,1378,0,-141202,0,22716418,0,...];
%e A158120 A157302 = [1,1,0,-5,0,183,0,-14352,0,1857199,0,-355082433,0,...].
%e A158120 ...
%o A158120 (PARI) {a(n)=local(A=[1, 1]); for(i=1, 2*n, if(#A%2==0, A=concat(A, t); A[ #A]=-subst(Vec(serreverse(x/Ser(A)))[ #A], t, 0)); if(#A%2==1, A=concat(A, t); A[ #A]=-subst(Vec(x/serreverse(x*Ser(A)))[ #A], t, 0))); (-1)^n*Vec(x/serreverse(x*Ser(A)))[2*n+1]}
%Y A158120 Cf. A157304, A157305, A157302, A157307, A158119.
%K A158120 nonn
%O A158120 0,2
%A A158120 _Paul D. Hanna_, Mar 12 2009