[seqfan] Re: binomial ( m!, n) ?

Robert Israel israel at math.ubc.ca
Wed Sep 1 07:13:57 CEST 2010


On Wed, 1 Sep 2010, Paul D Hanna wrote:

> A related sequence is A109892:
>   a(n) = least integer of the form (n!+1)(n!+2)...(n!+k)/n!.
> Is A109892 equivalent to binomial(n!+n,n)?

Yes.  Note that
(n!+1)(n!+2)...(n!+k) == k! mod n!
    == 0 mod n! if and only if k >= n (for n >= 2).

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada




More information about the SeqFan mailing list