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A071599
Product of elements in the simple continued fraction for (1+1/n)^n.
1
2, 8, 24, 216, 4320, 19008, 103488, 1292544, 1548288, 3264307200, 24710676480, 54623600640, 16562257920, 3345695539200, 8216950210560, 33673108783104000, 205682009702400000, 15655109317676236800, 12302792042521559040000
OFFSET
1,1
COMMENTS
It appears that lim n ->infinity a(n)^(1/A069887(n)) = K (Khinchin constant = 2.68...) - Benoit Cloitre, Jan 29 2006
LINKS
EXAMPLE
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
MATHEMATICA
Table[Times@@ContinuedFraction[(1+1/n)^n], {n, 20}] (* Harvey P. Dale, May 02 2019 *)
PROG
(PARI) for(n=1, 100, print1(prod(i=1, length(contfrac((1+1/n)^n)), component(contfrac((1+1/n)^n), i)), ", "))
CROSSREFS
Sequence in context: A330505 A214849 A141598 * A047695 A093842 A331001
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jun 01 2002
STATUS
approved