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A001340
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E.g.f.: 2*exp(x)/(1-x)^3.
(Formerly M1858 N0736)
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4
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2, 8, 38, 212, 1370, 10112, 84158, 780908, 8000882, 89763320, 1094915222, 14431179908, 204423631178, 3097603939952, 50001759773870, 856665220770332, 15526612798028258, 296825612428239848, 5969385443426556422, 125983618731675924020, 2784204907403441680442
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) = A001339 (n+1) - A001339 (n)..3-1=2, 11-3=8, 49-11=38... [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 06 2010]
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REFERENCES
| Biondi, E.; Divieti, L.; Guardabassi, G.; Counting paths, circuits, chains and cycles in graphs: A unified approach. Canad. J. Math. 22 1970 22-35.
Philip Feinsilver and John McSorley, Zeons, Permanents, the Johnson Scheme, and Generalized Derangements, International Journal of Combinatorics, Volume 2011, Article ID 539030, 29 pages; doi:10.1155/2011/539030.
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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FORMULA
| a(n) = floor((n+1)*(n+1)!*e) - floor(n*n!*e) [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 06 2010]
a(n) = {exp(1)*(n^2+n+1)*n!} for n>0, where {x} is the neareast integer, proposed by Simon Plouffe, March 1993.
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CROSSREFS
| Equals 2*A082030(n).
Sequence in context: A108246 A020031 A179323 * A058786 A096654 A191016
Adjacent sequences: A001337 A001338 A001339 * A001341 A001342 A001343
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Error in description corrected Jan 30 2008
More terms from N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2008
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