0,3

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]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

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.

(End)

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.

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).

Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. Algebra and its Applic. 373 (2003), p. 197-210.

Ed Sandifer, Divergent Series, How Euler Did It, MAA Online, June 2006. [From Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009]

E.g.f.: ( 1 - x )^(-3)*exp(-x).

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]

(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]

Cf. A000255, A000261, A001909, A001910, A090010, A055790, A090012-A090016.

A001710 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 25 2008]

Sequence in context: A006014 A121555 A097900 this_sequence A006154 A000987 A006957

Adjacent sequences: A000150 A000151 A000152 this_sequence A000154 A000155 A000156

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com).