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%I #16 Oct 05 2018 10:45:52
%S 1,2,6,23,108,605,3956,29649,250892,2367629,24662700,281153801,
%T 3482350724,46572620757,668943488084,10271127486065,167892667249116,
%U 2911049382788189,53365747562592092,1031352659792534169
%N a(n) = n! * {1 + Sum[i=1..n, 1/i*Sum(j=0..i-1, 1/j!)]}.
%C Number of {12,2*1}-avoiding signed permutations in the hyperoctahedral group B_n.
%H D. Daly and L. Pudwell, <a href="http://faculty.valpo.edu/lpudwell/slides/sandiego2013.pdf">Pattern avoidance in rook monoids</a>, 2013. - From _N. J. A. Sloane_, Feb 03 2013
%H T. Mansour and J. West, <a href="https://arxiv.org/abs/math/0207204">Avoiding 2-letter signed patterns</a>, arXiv:math/0207204 [math.CO], 2002.
%F E.g.f.: (exp(1)*(Ei(1, 1-x)-Ei(1, 1))+1)/(1-x). a(n) = n!*(1+Sum(A000522(i-1)/i!, i =1..n)). - _Vladeta Jovovic_, Apr 27 2004
%F Conjecture: a(n) -2*n*a(n-1) +(n^2-2)*a(n-2) -(n-2)^2*a(n-3)=0. - _R. J. Mathar_, May 30 2014
%t a[n_] := n! (1+Sum[1/i Sum[1/j!, {j, 0, i-1}], {i, 1, n}])
%t Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Oct 05 2018 *)
%o (PARI) a(n)=n!+n!*sum(i=1,n,1/i*sum(j=0,i-1,1/j!))
%Y Cf. A000774.
%Y Cf. A000522, A093344.
%Y Contribution from _Johannes W. Meijer_, Oct 16 2009: (Start)
%Y Equals row sums of A165675.
%Y (End)
%K nonn
%O 0,2
%A _Ralf Stephan_, Apr 26 2004
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