Search: id:A000354
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%I A000354 M3957 N1631
%S A000354 1,1,5,29,233,2329,27949,391285,6260561,112690097,2253801941,49583642701,
%T A000354 1190007424825,30940193045449,866325405272573,25989762158177189,
%U A000354 831672389061670049,28276861228096781665,1017967004211484139941
%N A000354 Expansion of e^{-x}/(1-2*x).
%C A000354 a(n) is the permanent of the n X n matrix with 1 on the diagonal and 
               2 elsewhere. - Yuval Dekel, Nov 01 2003
%C A000354 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2009: 
               (Start)
%C A000354 Starting with offset 1 = Lim_{k->inf.} M^k, where M = a tridiagonal matrix
%C A000354 with (1,0,0,0,...) in the main diagonal, (1,3,5,7,...) in the subdiagonal
%C A000354 and (2,4,6,8,...) in the subsubdiagonal. (End)
%C A000354 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]
%D A000354 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000354 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000354 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               83.
%D A000354 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.
%D A000354 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]
%H A000354 T. D. Noe, <a href="b000354.txt">Table of n, a(n) for n=0..100</a>
%H A000354 E. Lucas, <a href="http://gallica.bnf.fr/scripts/ConsultationTout.exe?E=0&O=N029021">
               Th\'{e}orie des Nombres</a>. Gauthier-Villars, Paris, 1891, Vol. 
               1, p. 223.
%F A000354 Inverse binomial transform of double factorials A000165 - Paul Barry 
               (pbarry(AT)wit.ie), May 26 2003
%F A000354 a(n)=sum{k=0..n, (-1)^(n+k)C(n, k)k!2^k } - Paul Barry (pbarry(AT)wit.ie), 
               May 26 2003
%F A000354 a(n)= Sum(k=0..n, A008290(n, k)*2^(n-k)) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Dec 13 2003
%F A000354 a(n)=2n*a(n-1)+(-1)^n, n>0, a(0)=1. - Paul Barry (pbarry(AT)wit.ie), 
               Aug 26 2004
%F A000354 a(n) = (2n-1)a(n-1) + (2n-2)a(n-2) [From Elizabeth McMahon, Gary Gordon 
               (mcmahone(AT)lafayette.edu), Jun 29 2009]
%p A000354 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
%t A000354 Table[ Gamma[ n, -1/2 ]*2^(n-1)/Exp[ 1/2 ], {n, 1, 24} ]; FunctionExpand[ 
               % ]
%Y A000354 Cf. A061714.
%Y A000354 Cf. A008290.
%Y A000354 Sequence in context: A057623 A087662 A113012 this_sequence A103815 A134752 
               A144015
%Y A000354 Adjacent sequences: A000351 A000352 A000353 this_sequence A000355 A000356 
               A000357
%K A000354 nonn,easy,nice
%O A000354 0,3
%A A000354 N. J. A. Sloane (njas(AT)research.att.com).

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