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

1, 3, 168, 3276000, 877449500928000, 207244701437748852512194560000, 4000516840149319128119305958853265913416777728000000, 796608816253064941944831363792070377592412324940256242675178274726476775424000000000

Offset: 1

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203483.

See A093883 for a guide to related sequences.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..16

Crossrefs

Cf. A000142, A203483, A203510, A306729, A325052.

Programs

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

Maple

a:= n-> mul(mul(i!+j!, i=1..j-1), j=2..n):
seq(a(n), n=1..10);  # Alois P. Heinz, Jul 23 2017

Mathematica

(* First program *)
f[j_]:= j!; z = 10;
v[n_]:= Product[Product[f[k] + f[j], {j, k-1}], {k, 2, n}]
d[n_]:= Product[(i-1)!, {i, n}]  (* A000178 *)
Table[v[n], {n, z}]              (* A203482 *)
Table[v[n+1]/v[n], {n, z-1}]     (* A203483 *)
Table[v[n]/d[n], {n, 10}]        (* A203510 *)
(* Second program *)
Table[Product[j!+k!, {j,n}, {k,j-1}], {n,15}] (* G. C. Greubel, Aug 29 2023 *)

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

Formula

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

Extensions

Name edited by Alois P. Heinz, Jul 23 2017