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Search: id:A000153
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| A000153 |
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a(n) = n*a(n-1) + (n-2)*a(n-2), with a(0) = 0, a(1) = 1.
(Formerly M1791 N0706)
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+0
16
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| 0, 1, 2, 7, 32, 181, 1214, 9403, 82508, 808393, 8743994, 103459471, 1328953592, 18414450877, 273749755382, 4345634192131, 73362643649444, 1312349454922513, 24796092486996338, 493435697986613143, 10315043624498196944
(list; graph; listen)
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OFFSET
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0,3
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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=2 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
Starting (1, 2, 7, 32,...) = inverse binomial transform of A001710 starting (1, 3, 12, 60, 360, 2520,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 25 2008]
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REFERENCES
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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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FORMULA
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E.g.f.: ( 1 - x )^(-3)*exp(-x).
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PROGRAM
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(Other) sage: it = sloane.A000153.gen(0, 1, 2) sage: [it.next() for i in range(21)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
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CROSSREFS
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Cf. A000255, A000261, A001909, A001910, A090010, A055790, A090012-A090016.
A001710 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 25 2008]
Adjacent sequences: A000150 A000151 A000152 this_sequence A000154 A000155 A000156
Sequence in context: A006014 A121555 A097900 this_sequence A006154 A000987 A006957
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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