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A203482 a(n) = Product_{1 <= i < j <= n} (i! + j!).

%I A203482 #25 Nov 20 2023 11:27:25
%S A203482 1,3,168,3276000,877449500928000,207244701437748852512194560000,
%T A203482 4000516840149319128119305958853265913416777728000000,
%U A203482 796608816253064941944831363792070377592412324940256242675178274726476775424000000000
%N A203482 a(n) = Product_{1 <= i < j <= n} (i! + j!).
%C A203482 Each term divides its successor, as in A203483.
%C A203482 See A093883 for a guide to related sequences.
%H A203482 G. C. Greubel, <a href="/A203482/b203482.txt">Table of n, a(n) for n = 1..16</a>
%F A203482 a(n) ~ c * n^(n^3/3 + n^2/4 - 7*n/12 + 5/8) * (2*Pi)^(n*(n-1)/4) / exp(4*n^3/9 - n^2/8 - n), where c = 0.488888619502150098591650327163991582267254151817880403495924251381414248582... - _Vaclav Kotesovec_, Nov 20 2023
%p A203482 a:= n-> mul(mul(i!+j!, i=1..j-1), j=2..n):
%p A203482 seq(a(n), n=1..10);  # _Alois P. Heinz_, Jul 23 2017
%t A203482 (* First program *)
%t A203482 f[j_]:= j!; z = 10;
%t A203482 v[n_]:= Product[Product[f[k] + f[j], {j, k-1}], {k, 2, n}]
%t A203482 d[n_]:= Product[(i-1)!, {i, n}]  (* A000178 *)
%t A203482 Table[v[n], {n, z}]              (* A203482 *)
%t A203482 Table[v[n+1]/v[n], {n, z-1}]     (* A203483 *)
%t A203482 Table[v[n]/d[n], {n, 10}]        (* A203510 *)
%t A203482 (* Second program *)
%t A203482 Table[Product[j!+k!, {j,n}, {k,j-1}], {n,15}] (* _G. C. Greubel_, Aug 29 2023 *)
%o A203482 (Magma) [(&*[(&*[Factorial(j) + Factorial(k): k in [1..j]])/(2*Factorial(j)): j in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Aug 29 2023
%o A203482 (SageMath) [product(product(factorial(j) + factorial(k) for k in range(1,j)) for j in range(1,n+1)) for n in range(1,16)] # _G. C. Greubel_, Aug 29 2023
%Y A203482 Cf. A000142, A203483, A203510, A306729, A325052.
%K A203482 nonn
%O A203482 1,2
%A A203482 _Clark Kimberling_, Jan 03 2012
%E A203482 Name edited by _Alois P. Heinz_, Jul 23 2017