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Product_{i=0..n} (i! + 1).
7

%I #21 Mar 15 2019 06:53:46

%S 2,4,12,84,2100,254100,183206100,923541950100,37238134969982100,

%T 13513011656042074430100,49036030210457135734021310100,

%U 1957361459740805606124917565020990100,937579272951542930363610919638075856505150100

%N Product_{i=0..n} (i! + 1).

%H Alois P. Heinz, <a href="/A217757/b217757.txt">Table of n, a(n) for n = 0..42</a>

%F a(n) ~ c * A000178(n), where c = A238695 = Product_{k>=0} (1 + 1/k!) = 7.364308272367257256372772509631... . - _Vaclav Kotesovec_, Jul 20 2015

%p a:= proc(n) a(n):= `if`(n=0, 2, a(n-1)*(n!+1)) end:

%p seq(a(n), n=0..14); # _Alois P. Heinz_, May 20 2013

%t Table[Product[i!+1,{i,0,n}],{n,0,12}] (* _Geoffrey Critzer_, May 04 2013 *)

%t Rest[FoldList[Times,1,Range[0,15]!+1]] (* _Harvey P. Dale_, May 28 2013 *)

%o (JavaScript)

%o function factorial(n) {

%o var i,c=1;

%o for (i=2;i<=n;i++) c*=i;

%o return c;

%o }

%o a=2;

%o for (j=1;j<10;j++) {

%o a*=(factorial(j)+1);

%o document.write(a+", ");

%o }

%Y Cf. A000142, A000178, A054640, A082480, A258325, A260231, A306729.

%K nonn

%O 0,1

%A _Jon Perry_, Mar 23 2013