[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
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