%I #29 Sep 08 2022 08:44:58
%S 1,9,34,125,462,1722,6468,24453,92950,354926,1360476,5231954,20177164,
%T 78004500,302211720,1173076245,4561139430,17761336230,69257611500,
%U 270391268070,1056823387620
%N a(n) = C(n)*(8n+1) where C(n)=Catalan numbers (A000108).
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H Vincenzo Librandi, <a href="/A050478/b050478.txt">Table of n, a(n) for n = 0..1000</a>
%F -(n+1)*(8*n-7)*a(n) + 2*(8*n+1)*(2*n-1)*a(n-1) = 0. - _R. J. Mathar_, Dec 03 2014
%F G.f.: (7 - 12*x - 7*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - _Ilya Gutkovskiy_, Jun 13 2017
%t Table[CatalanNumber[n](8n+1),{n,0,20}] (* _Harvey P. Dale_, May 20 2012 *)
%o (Magma)[Catalan(n)*(8*n+1):n in [0..30]]; // _Vincenzo Librandi_, Jan 27 2013
%o (Magma) R<x>:=PowerSeriesRing(Rationals(),30); (Coefficients(R!( (7-12*x-7*Sqrt(1-4*x))/(2*x*Sqrt(1-4*x)))))// _Marius A. Burtea_, Jan 05 2020
%Y Column k=8 of A330965.
%Y Cf. A016993, A000108, A051945.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Dec 24 1999