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%I #17 Nov 20 2023 04:31:38
%S 3,56,19500,267841728,236189890379520,19303349192505048268800,
%T 199126474924007956512865886208000,
%U 339543987407937097660189431863908761600000000,121553118121801544803671246298148699436481551316864204800000
%N a(n) = v(n+1)/v(n), where v = A203482.
%H G. C. Greubel, <a href="/A203483/b203483.txt">Table of n, a(n) for n = 1..29</a>
%F a(n) = Product_{k=1..n} (k! + (n+1)!). - _G. C. Greubel_, Aug 29 2023
%F From _Vaclav Kotesovec_, Nov 20 2023: (Start)
%F a(n) ~ (n+1)!^n.
%F a(n) ~ (2*Pi)^(n/2) * n^(n^2 + 3*n/2) / exp(n^2 - 13/12). (End)
%t (* First program *)
%t f[j_]:= j!; z = 10;
%t v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
%t d[n_]:= Product[(i-1)!, {i, n}] (* A000178 *)
%t Table[v[n], {n,z}] (* A203482 *)
%t Table[v[n+1]/v[n], {n,z-1}] (* this sequence *)
%t Table[v[n]/d[n], {n,10}] (* A203510 *)
%t (* Second program *)
%t Table[Product[k!+(n+1)!, {k,n}], {n,15}] (* _G. C. Greubel_, Aug 29 2023 *)
%o (Magma) [(&*[Factorial(k) + Factorial(n+1): k in [1..n]]): n in [1..16]]; // _G. C. Greubel_, Aug 29 2023
%o (SageMath) [product(factorial(k) + factorial(n+1) for k in range(1,n+1)) for n in range(1,16)] # _G. C. Greubel_, Aug 29 2023
%Y Cf. A000142, A093883, A203482, A203510, A323717.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 03 2012
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