# [seqfan] Re: Need help with puzzling sequence A118980

Fred Lunnon fred.lunnon at gmail.com
Tue Aug 13 00:14:28 CEST 2019

```T(n,n)  =  n!  =  n T(n-1,n-1) ;

T(n,n-1)  =  (n+1)T(n-1,n-2) - T(n-1,n-1)  =  n! (n+3)/2 ;

T(n,n-2)  =  ?

T(n,0)  =  2 T(n-1,0) + T(n-2,0) ;  fails for  n = 2  ?!

T(n,1)  =  ?

On 8/12/19, Neil Sloane <njasloane at gmail.com> wrote:
> Dear SeqFans, I have been cleaning up some old sequences with keyword
> "uned".
> At the end of the weekend, this one is still a mystery: A118980.  The
> puzzle boils down to this:
> What is the triangle?
>
> 1;
>
> 2, 1;
>
> 6, 5, 2;
>
> 14, 22, 18, 6;
>
> 34, 85, 118, 84, 24;
>
> 82, 311, 660, 780, 480, 120;
>
> ...
>
>
>
> *All that is needed is a plausible guess for a way to continue this
> triangle.*
>
>
> The left border is said to be the "companion Pell sequence A099425", and
> the right border is the factorials.
>
> There is an explicit definition in terms of a missing sequence referred to
> as "A118979" (different from the current A118979).
>
> There are more clues involving A118981, which also need editing, (Richard
> Mathar suggested a way to edit it in 2011, but I have not touched it
> because I did not want to disturb the crime scene).
>
> A118980 is a "cold case".  Richard Mathar worked on it in 2011, and I
> struggled with it over the weekend.  Now I'm calling in "The Wolf" - the
> combined minds of the Sequence Fans list. (The reference is to Pulp
> Fiction.)
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```