The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006347

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A006347

a(n) = (n+1) a(n-1) + (-1)^n.
(history; published version)

#43 by Susanna Cuyler at Tue Nov 07 18:16:26 EST 2017

STATUS

proposed

approved

#42 by Michel Marcus at Mon Nov 06 16:59:15 EST 2017

STATUS

editing

proposed

#41 by Michel Marcus at Mon Nov 06 16:59:11 EST 2017

FORMULA

a(n) = round((1/2 - exp(-1))*(n+1)!). - Benoit Cloitre, Sep 24 2006

a(n) = n(a(n-1) + a(n-2)), n > 2. - Gary Detlefs, Apr 10 2010

a(n) = 1/2*(n+1)! - floor(((n+1)!+1)/e). - Gary Detlefs, Apr 16 2010

STATUS

reviewed

editing

#40 by Alonso del Arte at Mon Nov 06 16:54:51 EST 2017

STATUS

proposed

reviewed

#39 by Alonso del Arte at Mon Nov 06 16:52:22 EST 2017

STATUS

editing

proposed

Discussion

Mon Nov 06

16:54

Alonso del Arte: I find Dr. Sharp's handwriting a bit hard to read, but I was able to verify that his letter is relevant to this entry, in fact being the letter that prompted the creation of this entry, published in the 1995 EIS as M3018.

#38 by Alonso del Arte at Mon Nov 06 16:52:15 EST 2017

COMMENTS

a(n) is a function of the subfactorials .. a(n) = (n+1)!/2 - A000166(n+1) - Gary Detlefs, Apr 16 2010

a(n) can be seen indeed as a shifted-forward version of the subfactorials = (or derangement numbers). - Olivier Gérard, Feb 23 2015

#37 by Alonso del Arte at Mon Nov 06 16:51:19 EST 2017

MATHEMATICA

RecurrenceTable[{a[1] == 0, a[n] == (n + 1) a[n - 1] + (-1)^n}, a, {n, 20}] (* Harvey P. Dale, Oct 19 2012 *)

STATUS

proposed

editing

#36 by Rachel Barnett at Mon Nov 06 15:02:40 EST 2017

STATUS

editing

proposed

#35 by Rachel Barnett at Mon Nov 06 15:02:29 EST 2017

LINKS

J. A. Sharp & N. J. A. Sloane, <a href="/A002026/a002026.pdf">Correspondence, 1977</a>

STATUS

approved

editing

#34 by Charles R Greathouse IV at Tue Oct 03 03:16:29 EDT 2017

STATUS

editing

approved