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%I #10 Apr 30 2014 01:37:14
%S 1,1,2,0,-1,0,2,0,-5,0,12,0,-30,0,82,0,-233,0,668,0,-1949,0,5802,0,
%T -17503,0,53302,0,-163783,0,507418,0,-1582869,0,4966790,0,-15667573,0,
%U 49658264,0,-158059506,0,505013014,0,-1619144976,0,5207596574
%N G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u * (u - 2) - (v + 2).
%F a(2*n) = 0 unless n=0. a(n) = A107088(n+1) unless n=0. a(2*n - 1) = A107087(n).
%e 1/x + 1 + 2*x - x^3 + 2*x^5 - 5*x^7 + 12*x^9 - 30*x^11 + 82*x^13 - ...
%o (PARI) {a(n) = local(A, m); if( n<-1, 0, if( n%2 == 0, n==0, A = 1 + O(x); m=1; while( 2*m <= n+1, A = sqrt(4*x + subst(A, x, x^2)); m*=2); polcoeff(A, (n+1)/2)))}
%Y Cf. A107087, A107088.
%K sign
%O -1,3
%A _Michael Somos_, Aug 04 2011