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A359714 Central terms of triangle A359670; a(n) = A359670(2*n,n) for n >= 0.

%I A359714 #7 Jan 18 2023 14:53:42
%S A359714 1,6,68,970,15627,271698,4980320,94919382,1864060550,37486601966,
%T A359714 768542230128,16010270917186,338044149765168,7220000851821450,
%U A359714 155743662496011552,3388779105788095886,74299386925266352272,1640069094618726916032,36421678762652448251540
%N A359714 Central terms of triangle A359670; a(n) = A359670(2*n,n) for n >= 0.
%C A359714 The g.f. G(x,y) of triangle A359670 satisfies: G(x,y) = 1/[Sum_{n=-oo..+oo} (-1)^n * (x*y*G(x,y) + x^n)^n].
%H A359714 Paul D. Hanna, <a href="/A359714/b359714.txt">Table of n, a(n) for n = 0..50</a>
%o A359714 (PARI) {a(n) = my(A=1); for(i=1,2*n,
%o A359714 A = 1/sum(m=-#A,#A, (-1)^m * (x*y*A + x^m + x*O(x^(2*n)) )^m ) );
%o A359714 polcoeff( polcoeff( A,2*n,x),n,y)}
%o A359714 for(n=0,25, print1( a(n),", "))
%o A359714 (PARI) {a(n) = my(A=[1]); for(i=1,2*n, A = concat(A,0);
%o A359714 A[#A] = polcoeff(-y + sum(m=-#A,#A, (-1)^m * x^m * (y*Ser(A) + x^(m-1))^(m+1) )/(-y),#A-1,x) ); polcoeff( A[2*n+1],n,y)}
%o A359714 for(n=0,25, print1(a(n),", "))
%Y A359714 Cf. A359670.
%K A359714 nonn
%O A359714 0,2
%A A359714 _Paul D. Hanna_, Jan 17 2023