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A006347
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a(n) = (n+1) a(n-1) + (-1)^n.
(Formerly M3018)
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1
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0, 1, 3, 16, 95, 666, 5327, 47944, 479439, 5273830, 63285959, 822717468, 11518044551, 172770668266, 2764330692255, 46993621768336, 845885191830047, 16071818644770894, 321436372895417879, 6750163830803775460
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) is a function of the subfactorials .. a(n)= (n+1)!/2 - A000166(n+1) [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 16 2010]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| E.g.f.: x(1-x/2-exp(-x))/(1-x)^2. a(n)=n(a(n-1)+a(n-2)), n>2.
a(n)=round((1/2-exp(-1))*(n+1)!) - Benoit Cloitre (abmt(AT)orange.fr), Sep 24 2006
a(n)= n(a(n-1)+a(n-2)) [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 10 2010]
a(n)=1/2*(n+1)! -floor(((n+1)!+1)/e) [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 16 2010]
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EXAMPLE
| a(2)=1/2*6-2=1, a(3)=1/2*24-9=3, a(4)=1/2*120-44=16... [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 16 2010]
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MAPLE
| a:=n->-n!*sum((-1)^k/k!, k=3..n): seq(a(n), n=2..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
seq(1/2*(n+1)! -floor(((n+1)!+1)/e), n=1..30); [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 16 2010]
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PROG
| (PARI) a(n)=if(n<2, 0, (n+1)*a(n-1)+(-1)^n)
(PARI) a(n)=round((1/2-exp(-1))*(n+1)!) - Benoit Cloitre (abmt(AT)orange.fr), Sep 24 2006
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CROSSREFS
| Sequence in context: A137644 A114174 A181067 * A000270 A157051 A000271
Adjacent sequences: A006344 A006345 A006346 * A006348 A006349 A006350
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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