%I A000153 M1791 N0706
%S A000153 0,1,2,7,32,181,1214,9403,82508,808393,8743994,103459471,1328953592,
%T A000153 18414450877,273749755382,4345634192131,73362643649444,1312349454922513,
%U A000153 24796092486996338,493435697986613143,10315043624498196944
%N A000153 a(n) = n*a(n-1) + (n-2)*a(n-2), with a(0) = 0, a(1) = 1.
%C A000153 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
%C A000153 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]
%C A000153 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 
               2009: (Start)
%C A000153 This sequence appears in Euler's analysis of the divergent series 1 - 
               1! + 2! - 3! + 4! ... , see Sandifer. For information about this 
               and related divergent series see A163940.
%C A000153 (End)
%D A000153 Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, 
               Cambridge NY (1991), Chapter 7.
%D A000153 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               188.
%D A000153 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000153 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000153 Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. 
               Algebra and its Applic. 373 (2003), p. 197-210.
%H A000153 Ed Sandifer, <a href="http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2032%20divergent%20series.pdf\
               ">Divergent Series</a>, How Euler Did It, MAA Online, June 2006. 
               [From Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009]
%F A000153 E.g.f.: ( 1 - x )^(-3)*exp(-x).
%F A000153 a(n) = round( GAMMA(n)*(1+3*n+n^2)*exp(-1)/2 ) for n>0 [From Mark van 
               Hoeij (hoeij(AT)math.fsu.edu), Nov 11 2009]
%o A000153 (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]
%Y A000153 Cf. A000255, A000261, A001909, A001910, A090010, A055790, A090012-A090016.
%Y A000153 A001710 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 25 2008]
%Y A000153 Sequence in context: A006014 A121555 A097900 this_sequence A006154 A000987 
               A006957
%Y A000153 Adjacent sequences: A000150 A000151 A000152 this_sequence A000154 A000155 
               A000156
%K A000153 nonn,easy,new
%O A000153 0,3
%A A000153 N. J. A. Sloane (njas(AT)research.att.com).