A359715 Column 2 of triangle A359670; a(n) = A359670(n+2,2) for n >= 0.

1, 12, 68, 284, 998, 3092, 8724, 22904, 56679, 133516, 301664, 657368, 1387854, 2849168, 5704476, 11166464, 21415632, 40312176, 74593476, 135864792, 243872632, 431835140, 755039948, 1304589104, 2229192801, 3769452152, 6311385252, 10469412968, 17214152072

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+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),", "))