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 A337726 #8 Sep 17 2020 20:31:25
%S A337726 1,61,20497,20292031,44317795705,180816606476401,1236785588298582841,
%T A337726 13142083661260741268467,205016505115667563788085201,
%U A337726 4494781858155895668489979946725,133764708098719455094261803214536001,5252940087036713001551661012234828759271
%N A337726 a(n) = (3*n+2)! * Sum_{k=0..n} 1 / (3*k+2)!.
%F A337726 E.g.f.: (exp(3*x/2) - 2 * sin(sqrt(3)*x/2 + Pi/6)) / (3*exp(x/2) * (1 - x^3)) = x^2/2! + 61*x^5/5! + 20497*x^8/8! + 20292031*x^11/11! + ...
%F A337726 a(n) = floor(c * (3*n+2)!), where c = (exp(3/2) - 2 * sin((3 * sqrt(3) + Pi) / 6))/(3 * sqrt(exp(1))) = A143821.
%t A337726 Table[(3 n + 2)! Sum[1/(3 k + 2)!, {k, 0, n}], {n, 0, 11}]
%t A337726 Table[(3 n + 2)! SeriesCoefficient[(Exp[3 x/2] - 2 Sin[Sqrt[3] x/2 + Pi/6])/(3 Exp[x/2] (1 - x^3)), {x, 0, 3 n + 2}], {n, 0, 11}]
%t A337726 Table[Floor[(Exp[3/2] - 2 Sin[(3 Sqrt[3] + Pi)/6])/(3 Sqrt[Exp[1]]) (3 n + 2)!], {n, 0, 11}]
%o A337726 (PARI) a(n) = (3*n+2)!*sum(k=0, n, 1/(3*k+2)!); \\ _Michel Marcus_, Sep 17 2020
%Y A337726 Cf. A000522, A051396, A051397, A087350, A100043, A143821, A330044, A337725, A337727, A337728, A337729, A337730.
%K A337726 nonn
%O A337726 0,2
%A A337726 _Ilya Gutkovskiy_, Sep 17 2020