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a(n) = C(n)*(11n+1) where C(n) = Catalan numbers (A000108).
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%I #26 Jul 08 2023 04:03:39

%S 1,12,46,170,630,2352,8844,33462,127270,486200,1864356,7171892,

%T 27665596,106977600,414538200,1609344270,6258307590,24373220520,

%U 95050101300,371125269900,1450670612820,5676173948640,22230262964520,87137141867100,341824599040860,1341897206800752

%N a(n) = C(n)*(11n+1) where C(n) = Catalan numbers (A000108).

%D Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H Andrew Howroyd, <a href="/A050490/b050490.txt">Table of n, a(n) for n = 0..200</a>

%F From _R. J. Mathar_, Feb 13 2015: (Start)

%F 5*(n+1)*a(n) + (-29*n-1)*a(n-1) + 18*(2*n-3)*a(n-2) = 0.

%F -(n+1)*(11*n-10)*a(n) + 2*(11*n+1)*(2*n-1)*a(n-1) = 0. (End)

%F G.f.: (5 - 9*x - 5*sqrt(1 - 4*x))/(x*sqrt(1 - 4*x)). - _Amiram Eldar_, Jul 08 2023

%t Table[CatalanNumber[n](11n+1),{n,0,20}] (* _Harvey P. Dale_, Jul 12 2018 *)

%o (Magma) [Catalan(n)*(11*n+1):n in [0..25] ]; // _Marius A. Burtea_, Jan 05 2020

%Y Column k=11 of A330965.

%Y Cf. A017281, A027810, A000108.

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Dec 27 1999

%E Terms a(21) and beyond from _Andrew Howroyd_, Jan 05 2020