|
%I #4 Oct 15 2013 22:32:21
%S 1,1,4,15,252,924,11440,43758,497420,13123110,54627300,1251677700,
%T 12033222880,52860229080,511738760544,10363194502115,197548686920970,
%U 925029565741050,17302625882942400,161884603662657876
%N a(n)=Product[p(n)-j, j=1..n]/n!=A090114(n)/n!.
%C It needs proof that A090114(n) is always divisible by n!, that is, these terms are integers.
%e n=5: p(5)=11, a(5)=(11-1)()(11-2)(11-3)(11-4)(11-5)/5!= 10.9.8.7.6/120=30240=252
%t Table[Apply[Times, Table[Prime[w]-j, {j, 1, w}]]/w!, {w, 1, 15}]
%Y Cf. A000142, A090114.
%K nonn
%O 1,3
%A _Labos Elemer_, Jan 08 2004
|
