A346506 - OEIS

A346506

G.f. A(x) satisfies: A(x) = (1 + x * A(x)^2) / (1 - x + x^2).

1, 2, 5, 17, 66, 274, 1190, 5341, 24577, 115326, 549747, 2654739, 12959468, 63848307, 317064921, 1585380283, 7975134892, 40332823042, 204947059412, 1045859173864, 5357606584326, 27540884494209, 142023060613755, 734506610474205, 3808771672620618, 19798640525731461, 103149287155802941

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(0) = 1, a(1) = 2; a(n) = 2 * a(n-1) + a(n-2) + Sum_{k=2..n-1} a(k) * a(n-k-1).

From Nikolaos Pantelidis, Jan 08 2023 (Start)

G.f.: 1/G(0), where G(k) = 1-(2*x-x^2)/(1-x/G(k+1)) (continued fraction).

G.f.: (1-x+x^2-sqrt(x^4-2*x^3+3*x^2-6*x+1))/(2*x).

(End)

MATHEMATICA