A079288 a(n) = (3^n)!.

1, 6, 362880, 10888869450418352160768000000

Offset: 0

Author

Cino Hilliard, Feb 08 2003

Keywords

• easy
• nonn

Comments

Next term is too large to include.

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

Crossrefs

Cf. A000142, A000244.

Programs

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,..

PARI

a(n) = (3^n)! \\ Michel Marcus, Sep 14 2015

Formula

a(n) = A000142(A000244(n)). - Michel Marcus, Sep 14 2015