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 A365269 #10 Aug 31 2023 09:50:23
%S A365269 1,2,14,476,99484,153802264,2049722772328,268353804798726416,
%T A365269 386893462638663037013264,6798536031341327693983294520096,
%U A365269 1595359632648441879172205168815801694176,5432770180592069558569584672506997142250856260032
%N A365269 a(n) = Product_{k=1..n} A002720(k).
%F A365269 log(a(n)) ~ log(BarnesG(n+2)) + 4*n^(3/2)/3 - n*log(n)/4 - (1/4 + log(2) + log(Pi)/2)*n + 55*sqrt(n)/24.
%F A365269 log(a(n)) ~ n^2*log(n)/2 - 3*n^2/4 + 4*n^(3/2)/3 + 3*n*log(n)/4 - (5/4 + log(2)/2)*n + 55*sqrt(n)/24.
%t A365269 Table[Product[k! * LaguerreL[k,-1], {k,1,n}], {n,0,15}]
%t A365269 Table[BarnesG[n+2] * Product[LaguerreL[k,-1], {k,1,n}], {n,0,15}]
%o A365269 (Python)
%o A365269 from math import prod, factorial, comb
%o A365269 def A365269(n): return prod(sum(factorial(m)*comb(k,m)**2 for m in range(k+1)) for k in range(1,n+1)) # _Chai Wah Wu_, Aug 31 2023
%Y A365269 Cf. A002720, A289897.
%K A365269 nonn
%O A365269 0,2
%A A365269 _Vaclav Kotesovec_, Aug 30 2023