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 A370057 #25 Feb 15 2025 12:41:44
%S A370057 1,3,30,546,14688,526680,23680800,1282554000,81339793920,
%T A370057 5915366392320,485415660038400,44376781223174400,4473125162795520000,
%U A370057 492902545595556096000,58949616073242166272000,7605168496387089788160000,1052810955815818170875904000
%N A370057 a(n) = 3*(4*n+2)!/(3*n+3)!.
%H A370057 Harvey P. Dale, <a href="/A370057/b370057.txt">Table of n, a(n) for n = 0..327</a>
%F A370057 E.g.f.: exp( 3/4 * Sum_{k>=1} binomial(4*k,k) * x^k/k ).
%F A370057 a(n) = A000142(n) * A006632(n+1).
%F A370057 D-finite with recurrence 3*(3*n+2)*(3*n+1)*(n+1)*a(n) -8*n*(4*n+1)*(2*n+1)*(4*n-1)*a(n-1)=0. - _R. J. Mathar_, Feb 22 2024
%F A370057 From _Seiichi Manyama_, Aug 31 2024: (Start)
%F A370057 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^3.
%F A370057 a(n) = 3 * Sum_{k=0..n} (3*n+3)^(k-1) * |Stirling1(n,k)|. (End)
%t A370057 Table[(3(4n+2)!)/(3n+3)!,{n,0,20}] (* _Harvey P. Dale_, Feb 15 2025 *)
%o A370057 (PARI) a(n) = 3*(4*n+2)!/(3*n+3)!;
%Y A370057 Cf. A365340, A370056, A370058.
%Y A370057 Cf. A000142, A006632.
%K A370057 nonn
%O A370057 0,2
%A A370057 _Seiichi Manyama_, Feb 08 2024