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 A065424 Catalan-like formula: a(n) = binomial(6m, 3m+1)/(9m+6). 1

%I

%S 1,33,1326,59432,2851425,143291610,7446255180,396893583792,

%T 21579377870484,1192183281903845,66734212415276406,

%U 3776778437640143208,215744630060724034270,12423227699242323077940

%N Catalan-like formula: a(n) = binomial(6m, 3m+1)/(9m+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

%o (MAGMA) [Binomial(6*n,3*n+1)/(9*n+6): n in [1..20]]; // _Vincenzo Librandi_, Nov 17 2011

%Y Cf. A000108, A065097.

%K nonn,easy

%O 1,2

%A _Len Smiley_, Nov 16 2001

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)