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A228401 The number of permutations of length n sortable by 2 block interchanges.

%I A228401 #30 Dec 31 2019 19:36:08
%S A228401 1,2,6,24,120,540,1996,6196,16732,40459,89519,184185,356721,656475,
%T A228401 1156443,1961563,3219019,5130856,7969228,12094622,17977422,26223198,
%U A228401 37602126,53082966,73872046,101457721,137660797,184691431,245213039,322413765,420086085,542715141
%N A228401 The number of permutations of length n sortable by 2 block interchanges.
%H A228401 Matthew House, <a href="/A228401/b228401.txt">Table of n, a(n) for n = 1..10000</a>
%H A228401 D. A. Christie, <a href="http://dx.doi.org/10.1016/S0020-0190(96)00155-X">Sorting Permutations by Block-Interchanges</a>, Inf. Process. Lett. 60 (1996), 165-169
%H A228401 C. Homberger, <a href="http://arxiv.org/abs/1410.2657">Patterns in Permutations and Involutions: A Structural and Enumerative Approach</a>, arXiv preprint 1410.2657 [math.CO], 2014.
%H A228401 C. Homberger, V. Vatter, <a href="http://arxiv.org/abs/1308.4946">On the effective and automatic enumeration of polynomial permutation classes</a>, arXiv preprint arXiv:1308.4946 [math.CO], 2013.
%H A228401 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A228401 G.f.: -x*(x^8 -8*x^7 +28*x^6 -54*x^5 +78*x^4 -42*x^3 +24*x^2 -7*x +1)/(x-1)^9.
%F A228401 a(n) = 1 + n*(n-1)*(n+1)*(n+2)*(3*n^4-10*n^3-11*n^2+50*n+216)/5760. [_Bruno Berselli_, Aug 22 2013]
%e A228401 The shortest permutations that cannot be sorted by 2 block interchanges are of length 7.
%t A228401 CoefficientList[Series[-(x^8 - 8 x^7 + 28 x^6 - 54 x^5 + 78 x^4 - 42 x^3 + 24 x^2 - 7 x + 1)/(x - 1)^9, {x, 0, 40}], x] (* _Bruno Berselli_, Aug 22 2013 *)
%t A228401 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,2,6,24,120,540,1996,6196,16732},40] (* _Harvey P. Dale_, Dec 31 2019 *)
%Y A228401 Cf. A145126, A256181.
%K A228401 nonn,easy
%O A228401 1,2
%A A228401 _Vincent Vatter_, Aug 21 2013