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A000904
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a(n) = (n + 1) a(n - 1) + (n + 2) a(n - 2) + a(n - 3); a(1)=0, a(2)=3, a(3)=13.
(Formerly M2955 N1193)
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1
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0, 3, 13, 83, 592, 4821, 43979, 444613, 4934720, 59661255, 780531033, 10987095719, 165586966816, 2660378564777, 45392022568023, 819716784789193, 15620010933562688, 313219935456042955, 6593238655510464741
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Menage numbers.
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 495.
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FORMULA
| G.f.: 1/(x+x^2)^2*Sum_{n>=0} n!*(x/(1+x)^2)^n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 29 2007
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PROG
| (Haskell)
a000904_list = 0 : 3 : 13 : zipWith (+) a000904_list
(zipWith (+) (zipWith (*) [6..] $ drop 1 a000904_list)
(zipWith (*) [5..] $ drop 2 a000904_list))
-- Reinhard Zumkeller, Nov 22 2011
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CROSSREFS
| Sequence in context: A089461 A000684 A057993 * A201304 A173998 A135743
Adjacent sequences: A000901 A000902 A000903 * A000905 A000906 A000907
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Nov 27 2001
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