A161581 - OEIS

%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,changed

%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