A277297 Diagonal of triangle A277295; a(n) = A277295(n+2,n).

2, 14, 76, 378, 1808, 8484, 39446, 182732, 846248, 3926338, 18276832, 85436832, 401313288, 1894847846, 8994916236, 42931067910, 206002472336, 993664391720, 4817140123620, 23464959242520, 114820471485840, 564248307992850, 2783898831160512, 13786409317705920, 68509284536815640, 341538385855855064, 1707729163812908528

Offset: 1

Author

Paul D. Hanna, Oct 11 2016

Keywords

• nonn

Comments

G.f. G(x,y) of triangle A277295 satisfies:

(1) G(x,y) = x + G( y*G(x,y) + (1-y)*x, y)^2.

(2) G( x - y*G(x,y)^2, y) = x + (1-y)*G(x,y)^2.

Crossrefs

Cf. A277295, A277296, A277298, A277299, A291822.

Programs

PARI

{A277295(n,k) = my(A=x); for(i=1, n, A = x + subst(A^2, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A,n,x),k,y)}
for(n=1,30,print1(A277295(n+2,n-1),", "))

Formula

a(n) = 2 * A291822(n) for n >= 1. - Paul D. Hanna, Jul 24 2023