A165976 Number of sequences of n pairs of balanced brackets of three types, round, square, and angle, such that no square brackets are allowed inside matching round brackets.

1, 3, 17, 117, 887, 7131, 59661, 513897, 4526603, 40588263, 369277481, 3400840845, 31644776383, 297079014771, 2810553697989, 26770090211793, 256510096740243, 2470981627433919, 23916768109136289, 232485664356533877

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

O.g.f.: ( 1 - x*G(2*x) - sqrt( (1 - x*G(2*x))^2 - 8*x ) )/(4*x) = (3 + sqrt(1-8*x) - sqrt(10 - 136*x + 6*sqrt(1-8*x)))/(16*x), where G(x)=(1-sqrt(1-4*x))/(2*x) is o.g.f. for Catalan numbers A000108.

Mathematica

CoefficientList[Series[(3 + Sqrt[1 - 8*x] - Sqrt[10 - 136*x + 6*Sqrt[1 - 8*x]])/(16*x), {x, 0, 50}], x] (* G. C. Greubel, Apr 20 2016 *)

Crossrefs

Sequence in context: A074554 A367945 A074544 * A368965 A344553 A121572

Adjacent sequences: A165973 A165974 A165975 * A165977 A165978 A165979

Keyword

nonn

Author

Max Alekseyev, Oct 02 2009

Status

approved