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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
1, 3, 17, 117, 887, 7131, 59661, 513897, 4526603, 40588263, 369277481, 3400840845, 31644776383, 297079014771, 2810553697989, 26770090211793, 256510096740243, 2470981627433919, 23916768109136289, 232485664356533877 (list; graph; refs; listen; history; text; internal format)
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: A112111 A074554 A074544 * A121572 A340993 A249924

Adjacent sequences:  A165973 A165974 A165975 * A165977 A165978 A165979

KEYWORD

nonn

AUTHOR

Max Alekseyev, Oct 02 2009

STATUS

approved

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Last modified March 6 04:14 EST 2021. Contains 341841 sequences. (Running on oeis4.)