A366736 - OEIS

%I #9 Nov 12 2023 19:35:47

%S 1,-2,14,-176,2615,-42444,734310,-13332898,251087228,-4863520344,

%T 96340129818,-1943639738074,39815238143374,-826201916477272,

%U 17334983283537509,-367213838120451038,7844257467257818627,-168807941163188191336,3656662240133060807499,-79675906058698383705100

%N Central terms of triangle A366730.

%C This sequence is defined by a(n) = [x^(2*n)*y^n] F(x,y) for n >= 0, where F(x,y) satisfies 0 = Sum_{n=-oo..+oo} x^n * F(x,y)^n * (y - x^(n-1))^(n+1), and F(x,y) is the g.f. of triangle A366730.

%H Paul D. Hanna, <a href="/A366736/b366736.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = A366730(2*n,n) for n >= 0.

%o (PARI) {A366730(n,k) = my(A=[1]); for(i=1,n, A = concat(A,0);

%o A[#A] = polcoeff( sum(n=-#A,#A, x^n * Ser(A)^n * (y - x^(n-1))^(n+1) ), #A-2)); polcoeff(A[n+1],k)}

%o for(n=0,20, print1(A366730(2*n,n),", "))

%Y Cf. A366730, A366731, A366732, A366733, A366734, A366735.

%K sign

%O 0,2

%A _Paul D. Hanna_, Oct 30 2023