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%I #22 Nov 22 2024 08:06:18
%S 21,231,3003,43758,692835,11685817,207157665,3823000545,72931087320,
%T 1430571328200,28734046963560,589047962752980,12292044987448215,
%U 260543149635912165,5599392250947235125,121830987186399315825
%N a(n) = (3n)!/(n!(n+1)!(n+2)!).
%C 3-d analog of the Catalan numbers A000108.
%H Winston de Greef, <a href="/A161581/b161581.txt">Table of n, a(n) for n = 3..704</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>.
%F a(n) = A006480(n)/((n+1)^2*(n+2)).
%F a(n) ~ 3^(3*n + 1/2) / (2*Pi*n^4). - _Vaclav Kotesovec_, Feb 21 2023
%F a(n) = (1/2)*A005789(n) for n >= 3. - _Peter Bala_, Mar 01 2023
%F D-finite with recurrence (n+2)*(n+1)*a(n) -3*(3*n-1)*(3*n-2)*a(n-1)=0. - _R. J. Mathar_, Nov 22 2024
%p A161581 := proc(n) (3*n)!/n!/(n+1)!/(n+2)! ; end: seq(A161581(n),n=3..40) ; # _R. J. Mathar_, Jun 16 2009
%p a := proc (n) options operator, arrow: factorial(3*n)/(factorial(n)*factorial(n+1)*factorial(n+2)) end proc: seq(a(n), n = 3 .. 20); # _Emeric Deutsch_, Jun 14 2009
%Y Cf. A000108, A005789, A006480.
%K nonn
%O 3,1
%A _Alexander Adamchuk_, Jun 14 2009
%E Repetitions of information contained in other sequences removed by _R. J. Mathar_, Jun 16 2009
%E More terms from _Emeric Deutsch_, Jun 14 2009