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 A064352 #45 Jan 07 2025 19:39:38
%S A064352 1,3,30,504,11880,360360,13366080,586051200,29654190720,1700755056000,
%T A064352 109027350432000,7725366544896000,599555620984320000,
%U A064352 50578512186237235200,4608264443634948096000,450974292794344230912000
%N A064352 a(n) = (3*n)!/(2*n)!.
%H A064352 Harry J. Smith, <a href="/A064352/b064352.txt">Table of n, a(n) for n = 0..100</a>
%H A064352 Guillaume Chapuy, <a href="https://arxiv.org/abs/2403.18719">On the scaling of random Tamari intervals and Schnyder woods of random triangulations (with an asymptotic D-finite trick)</a>, arXiv:2403.18719 [math.CO], 2024.
%H A064352 Karol A. Penson and Allan I. Solomon, <a href="https://doi.org/10.1142/9789812777850_0066">Coherent states from combinatorial sequences</a>, in: E. Kapuscik and A. Horzela (eds.), Quantum theory and symmetries, World Scientific, 2002, pp. 527-530; <a href="https://arxiv.org/abs/quant-ph/0111151">arXiv preprint</a>, arXiv:quant-ph/0111151, 2001.
%F A064352 Integral representation as n-th moment of a positive function on a positive half-axis: a(n) = Integral_{x>=0} (x^n*exp(-2*x/27)*(BesselK(1/3, 2*x/27) + BesselK(2/3, 2*x/27))*(sqrt(3)/(27*Pi))).
%F A064352 From Carleman's criterion Sum_{n>=1} a(n)^(-1/(2*n)) = infinity the above solution of the Stieltjes moment problem is unique. - _Karol A. Penson_, Jan 13 2018
%F A064352 a(n) = n! * [x^n] 1/(1 - x)^(2*n+1). - _Ilya Gutkovskiy_, Jan 23 2018
%F A064352 Sum_{n>=1} 1/a(n) = A248760. - _Amiram Eldar_, Nov 15 2020
%t A064352 Array[(3 #)!/(2 #)! &, 16, 0] (* _Michael De Vlieger_, Jan 13 2018 *)
%o A064352 (PARI) { f3=f2=1; for (n=0, 100, if (n, f3*=3*n*(3*n - 1)*(3*n - 2); f2*=2*n*(2*n - 1)); write("b064352.txt", n, " ", f3/f2) ) } \\ _Harry J. Smith_, Sep 12 2009
%o A064352 (Sage)
%o A064352 [falling_factorial(3*n, n) for n in (0..15)] # _Peter Luschny_, Jan 13 2018
%Y A064352 Cf. A001813, A166338, A248760.
%K A064352 nonn,easy
%O A064352 0,2
%A A064352 _Karol A. Penson_, Sep 19 2001
%E A064352 a(15) from _Harry J. Smith_, Sep 12 2009