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 A337725 #8 Sep 17 2020 20:31:14
%S A337725 1,25,5251,3780721,6487717237,21798729916321,126737815733490295,
%T A337725 1171057417377450325801,16160592359808814496053801,
%U A337725 317652603424402057734433512457,8567090714356123497097671830965291,307592825008242258039794809418977808065
%N A337725 a(n) = (3*n+1)! * Sum_{k=0..n} 1 / (3*k+1)!.
%F A337725 E.g.f.: (exp(3*x/2) - 2 * sin(Pi/6 - sqrt(3)*x/2)) / (3*exp(x/2) * (1 - x^3)) = x + 25*x^4/4! + 5251*x^7/7! + 3780721*x^10/10! + ...
%F A337725 a(n) = floor(c * (3*n+1)!), where c = (exp(3/2) + 2 * sin((3 * sqrt(3) - Pi) / 6))/(3 * sqrt(exp(1))) = A143820.
%t A337725 Table[(3 n + 1)! Sum[1/(3 k + 1)!, {k, 0, n}], {n, 0, 11}]
%t A337725 Table[(3 n + 1)! SeriesCoefficient[(Exp[3 x/2] - 2 Sin[Pi/6 - Sqrt[3] x/2])/(3 Exp[x/2] (1 - x^3)), {x, 0, 3 n + 1}], {n, 0, 11}]
%t A337725 Table[Floor[(Exp[3/2] + 2 Sin[(3 Sqrt[3] - Pi)/6])/(3 Sqrt[Exp[1]]) (3 n + 1)!], {n, 0, 11}]
%o A337725 (PARI) a(n) = (3*n+1)!*sum(k=0, n, 1/(3*k+1)!); \\ _Michel Marcus_, Sep 17 2020
%Y A337725 Cf. A000522, A051396, A051397, A087350, A100089, A143820, A330044, A337726, A337727, A337728, A337729, A337730.
%K A337725 nonn
%O A337725 0,2
%A A337725 _Ilya Gutkovskiy_, Sep 17 2020