A359718 - OEIS

%I #5 Jan 18 2023 14:54:27

%S 1,20,170,970,4410,17172,59545,188700,556085,1542640,4065868,10253720,

%T 24880705,58351000,132750390,293867786,634623035,1339924290,

%U 2771178885,5623152080,11211087225,21989506510,42478375740,80897833810,152022961870,282119268256,517394696690

%N Column 3 of triangle A359670; a(n) = A359670(n+3,3) for n >= 0.

%C 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].

%o (PARI) {a(n) = my(A=1); for(i=1,n+3,

%o A = 1/sum(m=-#A,#A, (-1)^m * (x*y*A + x^m + x*O(x^(n+3)) )^m ) );

%o polcoeff( polcoeff( A,n+3,x),3,y)}

%o for(n=0,30, print1( a(n),", "))

%o (PARI) {a(n) = my(A=[1]); for(i=1,n+3, A = concat(A,0);

%o 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[n+4],3,y)}

%o for(n=0,30, print1(a(n),", "))

%Y Cf. A359670.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 17 2023