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 A370056 #21 Aug 31 2024 08:31:55
%S A370056 1,2,18,312,8160,287280,12751200,684028800,43062243840,3113350732800,
%T A370056 254265345734400,23153103246873600,2326025084653670400,
%U A370056 255579097716214272000,30491180727539051520000,3925248256199788277760000,542357159056633603178496000
%N A370056 a(n) = 2*(4*n+1)!/(3*n+2)!.
%F A370056 E.g.f.: exp( 1/2 * Sum_{k>=1} binomial(4*k,k) * x^k/k ).
%F A370056 a(n) = A000142(n) * A069271(n).
%F A370056 D-finite with recurrence 3*(3*n+2)*(3*n+1)*a(n) -8*(4*n+1)*(2*n-1)*(4*n-1)*a(n-1)=0. - _R. J. Mathar_, Feb 22 2024
%F A370056 From _Seiichi Manyama_, Aug 31 2024: (Start)
%F A370056 E.g.f. satisfies A(x) = 1/(1 - x*A(x)^(3/2))^2.
%F A370056 a(n) = 2 * Sum_{k=0..n} (3*n+2)^(k-1) * |Stirling1(n,k)|. (End)
%o A370056 (PARI) a(n) = 2*(4*n+1)!/(3*n+2)!;
%Y A370056 Cf. A365340, A370057, A370058.
%Y A370056 Cf. A000142, A069271.
%K A370056 nonn
%O A370056 0,2
%A A370056 _Seiichi Manyama_, Feb 08 2024