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 A006347 a(n) = (n+1) a(n-1) + (-1)^n. (Formerly M3018) 4
 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; text; internal format)
 OFFSET 1,3 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Indranil Ghosh, Table of n, a(n) for n = 1..448 J. A. Sharp & N. J. A. Sloane, Correspondence, 1977 FORMULA E.g.f.: x(1 - x/2 - exp(-x))/(1-x)^2. 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 EXAMPLE a(2) = (1/2)*6 - 2 = 1, a(3) = (1/2)*24 - 9 = 3, a(4) = (1/2)*120 - 44 = 16 ... - Gary Detlefs, Apr 16 2010 MAPLE a:=n->-n!*sum((-1)^k/k!, k=3..n): seq(a(n), n=2..21); # Zerinvary Lajos, May 25 2007 seq(1/2*(n+1)! -floor(((n+1)!+1)/e), n=1..30); # Gary Detlefs, Apr 16 2010 MATHEMATICA RecurrenceTable[{a[1] == 0, a[n] == (n + 1) a[n - 1] + (-1)^n}, a, {n, 20}] (* Harvey P. Dale, Oct 19 2012 *) 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, Sep 24 2006 CROSSREFS Cf. A000166. Sequence in context: A137644 A114174 A181067 * A000270 A157051 A000271 Adjacent sequences: A006344 A006345 A006346 * A006348 A006349 A006350 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 18 20:35 EDT 2024. Contains 376002 sequences. (Running on oeis4.)