0,3

a(n) is the permanent of the n X n matrix with 1 on the diagonal and 2 elsewhere. - Yuval Dekel, Nov 01 2003

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2009: (Start)

Starting with offset 1 = Lim_{k->inf.} M^k, where M = a tridiagonal matrix

with (1,0,0,0,...) in the main diagonal, (1,3,5,7,...) in the subdiagonal

and (2,4,6,8,...) in the subsubdiagonal. (End)

a(n) is also the number of (n-1)-dimensional facet derangements for the n-dimensional hypercube. [From Elizabeth McMahon, Gary Gordon (mcmahone(AT)lafayette.edu), Jun 29 2009]

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).

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 83.

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

arXiv:0906.4253 : Moving faces to other places: Facet derangements. Authors: Gary Gordon, Elizabeth McMahon [From Elizabeth McMahon, Gary Gordon (mcmahone(AT)lafayette.edu), Jun 29 2009]

T. D. Noe, Table of n, a(n) for n=0..100

E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 223.

Inverse binomial transform of double factorials A000165 - Paul Barry (pbarry(AT)wit.ie), May 26 2003

a(n)=sum{k=0..n, (-1)^(n+k)C(n, k)k!2^k } - Paul Barry (pbarry(AT)wit.ie), May 26 2003

a(n)= Sum(k=0..n, A008290(n, k)*2^(n-k)) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 13 2003

a(n)=2n*a(n-1)+(-1)^n, n>0, a(0)=1. - Paul Barry (pbarry(AT)wit.ie), Aug 26 2004

a(n) = (2n-1)a(n-1) + (2n-2)a(n-2) [From Elizabeth McMahon, Gary Gordon (mcmahone(AT)lafayette.edu), Jun 29 2009]

BB := (x, k)->k!*sum(sum(x^j/((k-j)!^2*j!), j=1..k), m=1..k): R := (x, n, k)->BB(x, k)^n: f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k): > seq(abs(f(0, n, 2)/2!^n), n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2007

Table[ Gamma[ n, -1/2 ]*2^(n-1)/Exp[ 1/2 ], {n, 1, 24} ]; FunctionExpand[ % ]

Cf. A061714.

Cf. A008290.

Sequence in context: A057623 A087662 A113012 this_sequence A103815 A134752 A144015

Adjacent sequences: A000351 A000352 A000353 this_sequence A000355 A000356 A000357

nonn,easy,nice

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