OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10
N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]
FORMULA
a(n+1) = (n+1)!*a(n)^2 + a(n), with a(1) = 2.
EXAMPLE
The first few sums are 0/1, 1/2, 9/10, 609/610, 8931009/8931010, 9571552763343009/9571552763343010, ...
MAPLE
s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+n!/b(n)) end:
b:= proc(n) b(n):= 1+floor(n!/(1-s(n-1))) end:
a:= n-> denom(s(n)):
seq(a(n), n=0..7); # Alois P. Heinz, Oct 18 2024
CROSSREFS
KEYWORD
nonn,frac,changed
AUTHOR
N. J. A. Sloane, Sep 04 2024
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 18 2024
STATUS
approved