A071599 Product of elements in the simple continued fraction for (1+1/n)^n.

2, 8, 24, 216, 4320, 19008, 103488, 1292544, 1548288, 3264307200, 24710676480, 54623600640, 16562257920, 3345695539200, 8216950210560, 33673108783104000, 205682009702400000, 15655109317676236800, 12302792042521559040000

Offset: 1

Author

Benoit Cloitre, Jun 01 2002

Keywords

• easy
• nonn

Comments

It appears that lim_{n->oo} a(n)^(1/A069887(n)) = A002210 (Khinchin constant = 2.68...). - Benoit Cloitre, Jan 29 2006

Examples

			The continued fraction for (1+1/5)^5 is [2, 2, 20, 1, 9, 2, 3] and 2*2*20*1*9*2*3=4320 hence a(5)=4320
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..449

Programs

Mathematica

Table[Times@@ContinuedFraction[(1+1/n)^n],{n,20}] (* Harvey P. Dale, May 02 2019 *)

PARI

a(n) = prod(i=1, length(contfrac((1+1/n)^n)), component(contfrac((1+1/n)^n), i));