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 A370054 #17 Aug 31 2024 08:31:10
%S A370054 1,2,14,180,3432,87360,2790720,107442720,4845456000,250637587200,
%T A370054 14631376032000,951675588864000,68257101465907200,5352223511771136000,
%U A370054 455529588681155788800,41824228767217408512000,4120692998969056333824000,433653882272457833226240000
%N A370054 a(n) = 2*(3*n+1)!/(2*n+2)!.
%F A370054 E.g.f.: exp( 2/3 * Sum_{k>=1} binomial(3*k,k) * x^k/k ).
%F A370054 a(n) = A000142(n)*A006013(n). - _Alois P. Heinz_, Feb 08 2024
%F A370054 From _Seiichi Manyama_, Aug 31 2024: (Start)
%F A370054 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^2.
%F A370054 a(n) = 2 * Sum_{k=0..n} (2*n+2)^(k-1) * |Stirling1(n,k)|. (End)
%o A370054 (PARI) a(n) = 2*(3*n+1)!/(2*n+2)!;
%Y A370054 Cf. A001763, A370055.
%Y A370054 Cf. A000142, A006013.
%K A370054 nonn
%O A370054 0,2
%A A370054 _Seiichi Manyama_, Feb 08 2024