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 A368853 #9 Jan 08 2024 09:00:59
%S A368853 1,1,7,83,1661,49829,2092819,117197863,8438246137,759442152329,
%T A368853 83538636756191,11027100051817211,1720227608083484917,
%U A368853 313081424671194254893,65747099180950793527531,15779303803428190446607439,4291970634532467801477223409
%N A368853 a(n) = n! * (n+1)! * Sum_{k=0..n} (-1)^k/(k! * (k+1)!).
%F A368853 a(n) = n * (n+1) * a(n-1) + (-1)^n.
%F A368853 a(n) ~ BesselJ(1,2) * n! * (n+1)!. - _Vaclav Kotesovec_, Jan 08 2024
%o A368853 (PARI) a(n) = n!*(n+1)!*sum(k=0, n, (-1)^k/(k!*(k+1)!));
%Y A368853 Cf. A000166, A368854.
%Y A368853 Cf. A228229.
%K A368853 nonn,easy
%O A368853 0,3
%A A368853 _Seiichi Manyama_, Jan 07 2024