A359718 Column 3 of triangle A359670; a(n) = A359670(n+3,3) for n >= 0.

1, 20, 170, 970, 4410, 17172, 59545, 188700, 556085, 1542640, 4065868, 10253720, 24880705, 58351000, 132750390, 293867786, 634623035, 1339924290, 2771178885, 5623152080, 11211087225, 21989506510, 42478375740, 80897833810, 152022961870, 282119268256, 517394696690

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].

Crossrefs

Cf. A359670.

Programs

PARI

{a(n) = my(A=1); for(i=1,n+3,
A = 1/sum(m=-#A,#A, (-1)^m * (x*y*A + x^m + x*O(x^(n+3)) )^m ) );
polcoeff( polcoeff( A,n+3,x),3,y)}
for(n=0,30, print1( a(n),", "))

PARI

{a(n) = my(A=[1]); for(i=1,n+3, 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[n+4],3,y)}
for(n=0,30, print1(a(n),", "))