A000522 vs A131178 ?

[David W. Cantrell]

My quick guess is that a formula in closed form for A000522 is 

floor(e (n - 1)! - 1/n), valid for n >= 1.

David W. Cantrell


----- Original Message ----- 
From: "Alexander Povolotsky" <apovolot at gmail.com>
To: <njas at research.att.com>
Cc: "seqfan" <seqfan at ext.jussieu.fr>
Sent: Monday, October 29, 2007 22:58
Subject: A000522 vs A131178 ?


> A000522  Total number of arrangements of a set with n elements:
> a(n) = Sum_{k=0..n} n!/k!.
> 
> 1, 2, 5, 16, 65, 326, 1957, 13700, 109601, 986410, 9864101,
> 108505112, 1302061345, 16926797486, 236975164805, 3554627472076,
> 56874039553217, 966858672404690, 17403456103284421,
> 330665665962404000, 6613313319248080001
> 
> AUTHOR   njas
> 
> A131178  Floor( e n! ).  
> 2, 2, 5, 16, 65, 326, 1957, 13700, 109601, 986410, 9864101,
> 108505112, 1302061345, 16926797486, 236975164805, 3554627472076,
> 56874039553217, 966858672404690, 17403456103284421,
> 330665665962404000, 6613313319248080001, 138879579704209680022
> 
> AUTHOR   njas