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 A277299 Central terms of triangle A277295 in even-indexed rows; a(n) = A277295(2*n,n-1). 4

%I #7 Oct 11 2016 18:41:32

%S 1,14,698,56410,6036632,784844330,118467338692,20204403241014,

%T 3825143045741850,794096638401382028,179152196191253429864,

%U 43621984527307144281094,11400895235718650585287660,3183846191638117842792003252,946381984098376099573619213864,298412976572690317096982653746772

%N Central terms of triangle A277295 in even-indexed rows; a(n) = A277295(2*n,n-1).

%C G.f. G(x,y) of triangle A277295 satisfies:

%C (1) G(x,y) = x + G( y*G(x,y) + (1-y)*x, y)^2.

%C (2) G( x - y*G(x,y)^2, y) = x + (1-y)*G(x,y)^2.

%o (PARI) {A277295(n,k) = my(A=x); for(i=1, n, A = x + subst(A^2, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A,n,x),k,y)}

%o for(n=1,20,print1(A277295(2*n,n-1),", "))

%Y Cf. A277295, A277296, A277297, A277298.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 11 2016

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