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 A348084 #26 Jun 09 2025 11:30:09
%S A348084 1,3,65,2646,159027,12662650,1256328866,149304004500,20677182465555,
%T A348084 3270191625210510,581535955088511150,114860168436414644100,
%U A348084 24947615188488584876910,5909902157669174347277556,1516413100622001261250104100,418965782063742792530650053000
%N A348084 a(n) = [x^n] Product_{k=1..2*n} 1/(1 - k * x).
%H A348084 Seiichi Manyama, <a href="/A348084/b348084.txt">Table of n, a(n) for n = 0..300</a>
%F A348084 a(n) = S2(3*n,2*n), where S2(n,k) is Stirling numbers of the second kind.
%F A348084 a(n) = (1/(2*n)!) * Sum_{k=0..2*n} (-1)^k * k^(3*n) * binomial(2*n,k).
%F A348084 a(n) ~ 3^(3*n) * n^(n - 1/2) / (sqrt(Pi*(1-c)) * 2^(n+1) * exp(n) * (3 - 2*c)^n * c^(2*n)), where c = -LambertW(-3*exp(-3/2)/2) = 0.62578253420128292093838... - _Vaclav Kotesovec_, Oct 02 2021
%o A348084 (PARI) a(n) = polcoef(1/prod(k=1, 2*n, 1-k*x+x*O(x^n)), n);
%o A348084 (PARI) a(n) = stirling(3*n, 2*n, 2);
%o A348084 (PARI) a(n) = sum(k=0, 2*n, (-1)^k*k^(3*n)*binomial(2*n, k))/(2*n)!;
%o A348084 (Python)
%o A348084 from sympy.functions.combinatorial.numbers import stirling
%o A348084 def A348084(n): return stirling(3*n,2*n) # _Chai Wah Wu_, Jun 09 2025
%Y A348084 Cf. A007820 (S2(2*n,n)), A008277 (S2(n,k)), A129505, A348085.
%K A348084 nonn
%O A348084 0,2
%A A348084 _Seiichi Manyama_, Sep 28 2021