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 A383881 #11 May 21 2025 11:14:40
%S A383881 1,6,266,22275,2757118,452329200,92484925445,22653141490980,
%T A383881 6466506598695390,2108114165258886708,772778072287000494520,
%U A383881 314641228029527540596455,140880584836935832288402135,68799366730032076856334789900,36392216443342587869022660451080,20728132932716479897744043460870000
%N A383881 a(n) = [x^n] Product_{k=1..3*n} 1/(1 - k*x).
%H A383881 Vincenzo Librandi, <a href="/A383881/b383881.txt">Table of n, a(n) for n = 0..200</a>
%F A383881 a(n) = Stirling2(4*n,3*n).
%F A383881 a(n) ~ (-1)^(3*n) * 4^(4*n) * n^(n - 1/2) / (sqrt(2*Pi*(1 + w)) * exp(n) * 3^(3*n + 1/2) * w^(3*n) * (4/3 + w)^n), where w = LambertW(-4/(3*exp(4/3))).
%t A383881 Table[SeriesCoefficient[Product[1/(1-k*x), {k, 1, 3*n}], {x, 0, n}], {n, 0, 15}]
%t A383881 Table[StirlingS2[4*n, 3*n], {n, 0, 15}]
%t A383881 Table[SeriesCoefficient[(-1)^n/(Pochhammer[1 - 1/x, 3*n]*x^(3*n)), {x, 0, n}], {n, 0, 15}]
%o A383881 (Magma) [&+[Abs(StirlingSecond(4*n, 3*n))]: n in [0..15]]; // _Vincenzo Librandi_, May 21 2025
%Y A383881 Cf. A007820, A348084, A383882.
%Y A383881 Cf. A217913.
%K A383881 nonn
%O A383881 0,2
%A A383881 _Vaclav Kotesovec_, May 13 2025