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Search: id:A000261
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| A000261 |
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a(n) = n*a(n-1) + (n-3)*a(n-2).
(Formerly M2949 N1189)
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+0
15
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| 0, 1, 3, 13, 71, 465, 3539, 30637, 296967, 3184129, 37401155, 477471021, 6581134823, 97388068753, 1539794649171, 25902759280525, 461904032857319, 8702813980639617, 172743930157869827, 3602826440828270029
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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With offset 1, permanent of (0,1)-matrix of size n X (n+d) with d=3 and n zeros not on a line. This is a special case of Theorem 2.3 of Seok-Zun Song et al. Extremes of permanents of (0,1)-matrices, p. 201-202. - Jaap Spies (j.spies(AT)hccnet.nl), Dec 12 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 188.
Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. Algebra and its Applic. 373 (2003), p. 197-210.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..102
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FORMULA
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E.g.f.: e^(-x) (1 - x )^(-4).
(1/6)*Sum_{k=0..n} (-1)^k*(n-k+1)*(n-k+2)*(n-k+3)*n!/k! = (1/6)*(A000166(n)+3*A000166(n+1)+3*A000166(n+2)+A000166(n+3)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2003
a(n) = round( GAMMA(n)*(n^3+6*n^2+8*n+1)*exp(-1)/6 ) for n>0 [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 11 2009]
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CROSSREFS
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Cf. A000255, A000153, A001909, A001910, A090010, A055790, A090012-A090016.
Sequence in context: A126390 A003319 A158882 this_sequence A111140 A137983 A059032
Adjacent sequences: A000258 A000259 A000260 this_sequence A000262 A000263 A000264
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2003
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