Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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