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%I #26 Mar 10 2023 10:08:21
%S 1,33,1326,59432,2851425,143291610,7446255180,396893583792,
%T 21579377870484,1192183281903845,66734212415276406,
%U 3776778437640143208,215744630060724034270,12423227699242323077940
%N Catalan-like formula: a(n) = binomial(6*n, 3*n+1)/(9*n+6).
%H Vincenzo Librandi, <a href="/A065424/b065424.txt">Table of n, a(n) for n = 1..100</a>
%F G.f.: A*sqrt((A+1)*(1+9*A)) where A=x*(1+9*A)^3*(1+A). - _Mark van Hoeij_, Nov 16 2011
%F -(n-1)*(3*n+2)*(3*n+1)*a(n) + 8*(6*n-5)*(6*n-1)*(2*n-1)*a(n-1) = 0. - _R. J. Mathar_, Oct 31 2015
%F a(n) = (1/9)*A000245(3*n) = n*A000108(3*n)/(3*n + 2) for n >= 1. - _Peter Bala_, Mar 08 2023
%o (Magma) [Binomial(6*n,3*n+1)/(9*n+6): n in [1..20]]; // _Vincenzo Librandi_, Nov 17 2011
%Y Cf. A000108, A000245, A065097.
%K nonn,easy
%O 1,2
%A _Len Smiley_, Nov 16 2001
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