OFFSET
0,2
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].
PROG
(PARI) {a(n) = my(A=1); for(i=1, n+2,
A = 1/sum(m=-#A, #A, (-1)^m * (x*y*A + x^m + x*O(x^(n+2)) )^m ) );
polcoeff( polcoeff( A, n+2, x), 2, y)}
for(n=0, 30, print1( a(n), ", "))
(PARI) {a(n) = my(A=[1]); for(i=1, n+2, 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+3], 2, y)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 17 2023
STATUS
approved