This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A161581 #23 Feb 16 2025 08:33:10 %S A161581 21,231,3003,43758,692835,11685817,207157665,3823000545,72931087320, %T A161581 1430571328200,28734046963560,589047962752980,12292044987448215, %U A161581 260543149635912165,5599392250947235125,121830987186399315825 %N A161581 a(n) = (3n)!/(n!(n+1)!(n+2)!). %C A161581 3-d analog of the Catalan numbers A000108. %H A161581 Winston de Greef, <a href="/A161581/b161581.txt">Table of n, a(n) for n = 3..704</a> %H A161581 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>. %H A161581 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>. %H A161581 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>. %F A161581 a(n) = A006480(n)/((n+1)^2*(n+2)). %F A161581 a(n) ~ 3^(3*n + 1/2) / (2*Pi*n^4). - _Vaclav Kotesovec_, Feb 21 2023 %F A161581 a(n) = (1/2)*A005789(n) for n >= 3. - _Peter Bala_, Mar 01 2023 %F A161581 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 A161581 := proc(n) (3*n)!/n!/(n+1)!/(n+2)! ; end: seq(A161581(n),n=3..40) ; # _R. J. Mathar_, Jun 16 2009 %p A161581 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 A161581 Cf. A000108, A005789, A006480. %K A161581 nonn %O A161581 3,1 %A A161581 _Alexander Adamchuk_, Jun 14 2009 %E A161581 Repetitions of information contained in other sequences removed by _R. J. Mathar_, Jun 16 2009 %E A161581 More terms from _Emeric Deutsch_, Jun 14 2009