[seqfan] Re: formula for A062204
Max Alekseyev
maxale at gmail.com
Fri Mar 13 04:17:39 CET 2009
On Thu, Mar 12, 2009 at 7:11 PM, Ray Chandler
<rayjchandler at sbcglobal.net> wrote:
> Covington paper available at following link:
>
> http://www.ai.uga.edu/mc/number.pdf
Thanks, this link seems to work not from every PC but I eventually was
able to download the paper.
Now I see what the sequences A001850 (y=2), A062208 (y=3), A062205
(y=4), A062204 (y=7) are supposed to mean.
But the general formula for A(n,y) given in A062204 is wrong.
Correct formula can be obtained by the inclusion-exclusion principle:
B(n,y) = sum(k=n,n*y, sum(t=0,k, (-1)^t * binomial(k,t) * binomial(k-t,n)^y ))
For y=2 it well reproduces the values of A001850 but for the other
sequences it gives different values:
A062208 (y=3) for n=0..10:
1, 13, 409, 16081, 699121, 32193253, 1538743249, 75494983297,
3776339263873, 191731486403293, 9850349744182729
A062205 (y=4) for n=0..10:
1, 75, 23917, 10681263, 5552351121, 3147728203035, 1887593866439485,
1177359342144641535, 756051015055329306625, 496505991344667030490635,
331910222316215755702672557
A062204 (y=7) for n=0..10:
1, 47293, 58514835289, 143743469278461361, 480086443888959812703121,
1909946024633189859690880523893,
8508048612432263410111274212273801489,
41020870889694863957061607086939138327565057,
209691630817770382144439647416526247292909726379393,
1121241285685659360225420876424590015281785102622410968973,
6213239693876579408708842528154872834110410698303331900339282569
So, the sequences A062208, A062205, A062204 are completely wrong (as
they don't match the definition and there is no way to reproduce
them). I suggest to replace them with the above sequences.
Regards,
Max
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