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Template:Sequence of the Day for May 19

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Intended for: May 19, 2014

Timetable

  • First draft entered by Alonso del Arte on May 9, 2013
  • Draft reviewed by Daniel Forgues on May 18, 2015 (May 15, 2016) ✓
  • Draft to be approved by April 19, 2014
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A001142:
n

k  = 1
k  2 k   − 1 −  n
, or
n

k  = 0
, n   ≥   0
.
{ 1, 1, 2, 9, 96, 2500, 162000, ... }
The second formula above shows that this sequence is also the products of consecutive horizontal rows of Pascal’s triangle. As it happens, these numbers are related to Euler’s number
e
thus:
     
  
a (n + 1)
a (n)
  
  
a (n)
a (n − 1)
  
=
a (n − 1) a (n + 1)
a (n) 2
= e.