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

1, 6, 68, 970, 15627, 271698, 4980320, 94919382, 1864060550, 37486601966, 768542230128, 16010270917186, 338044149765168, 7220000851821450, 155743662496011552, 3388779105788095886, 74299386925266352272, 1640069094618726916032, 36421678762652448251540

Offset: 0

Author

Paul D. Hanna, Jan 17 2023

Keywords

• nonn

Comments

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].

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A359670.

Programs

PARI

{a(n) = my(A=1); for(i=1,2*n,
A = 1/sum(m=-#A,#A, (-1)^m * (x*y*A + x^m + x*O(x^(2*n)) )^m ) );
polcoeff( polcoeff( A,2*n,x),n,y)}
for(n=0,25, print1( a(n),", "))

PARI

{a(n) = my(A=[1]); for(i=1,2*n, A = concat(A,0);
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)}
for(n=0,25, print1(a(n),", "))