A079288 - OEIS

%I #12 Sep 14 2015 18:42:03

%S 1,6,362880,10888869450418352160768000000

%N a(n) = (3^n)!.

%C Next term is too large to include.

%C Sum_{n>0} 1/a(n) = 0.1666694223985890... or about 1/6. This is evident since 1/3! =0.166666666666.. 1/9! =0.0000027557319223985.. 1/27!=0.00000000000000000000000000091836898637955461.. for example shows that succeeding terms have little influence on the first term 1/6. A000722 has the same property of about 1/2 but it is not evident since in 1/2! + 1/4! + 1/8! 1/4! and 1/8! have an immediate effect on the first term 1/2. So the limit of sum(1/(x^n)!) -> 1/x! as x,n -> oo

%F a(n) = A000142(A000244(n)). - _Michel Marcus_, Sep 14 2015

%o (PARI) atonfact(a,n) = {sr=0; for(x=1,n, y =(a^x)!; \-((a-1)^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) } usage: ? atonfact(3,n) n=1,2,..

%o (PARI) a(n) = (3^n)! \\ _Michel Marcus_, Sep 14 2015

%Y Cf. A000142, A000244.

%K easy,nonn

%O 0,2

%A _Cino Hilliard_, Feb 08 2003