[Fwd: A003316 confusion]

[David W. Wilson]

"David W. Wilson" wrote:
> 
> Solution to my recent confusion:
> 
> Emeric Deutsch points out that A003316 is concerned with SUBSEQUENCES
> of not necessarily adjacent elements, while A008304 is concerned with
> RUNS of adjacent elements.  My misunderstanding of A003316 explains
> why I was unable to reconcile it with A008304.
> 
> In fact, A003316 is obtainable from A047874.  The analogous sequence
> obtained from A008304 does not yet exist in the EIS, but begins
> 
>     1,3,12,55,299,1900,13942
> 
> I will try to supply more details later.

The extend sequence is

1 3 12 55 299 1900 13942 115932 1078361 11092265 125040100 1532995992
20310212672 289186696338 4404156016584 71441907922793 1229835421590959
22393298253477006 430019590699868644 8685717780508953928

This is the total number of longest runs of all permutations of length
n, starting with n = 1.  NJAS: I am submitting this sequence.