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%I #11 May 03 2019 09:40:25
%S 10,148,1260,8160,44790,220180,1001000,4295168,17633122,69921460,
%T 269652100,1016524352,3760334958,13690636212,49172875520,174559419680,
%U 613383654170,2136135472020,7380351046300,25319087913760,86308819112550,292526411823828,986294675689560
%N Number of permutations of [n] with exactly 3 descents which avoid the pattern 4321.
%H Colin Barker, <a href="/A095889/b095889.txt">Table of n, a(n) for n = 5..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (22,-216,1248,-4710,12180,-22004,27752,-23937,13446,-4428,648).
%F G.f.: 2*x^5*(5 - 36*x + 82*x^2 - 36*x^3 - 87*x^4 + 80*x^5) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^4).
%F a(n) = (n*(27 + 81*2^n - 115*3^n + 3*(27*2^n+2*3^n)*n + (-27+3^n)*n^2)) / 162. - _Colin Barker_, May 03 2019
%o (PARI) Vec(2*x^5*(5 - 36*x + 82*x^2 - 36*x^3 - 87*x^4 + 80*x^5) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^4) + O(x^30)) \\ _Colin Barker_, Nov 03 2017
%Y Cf. A000295, A000460.
%K nonn,easy
%O 5,1
%A _Mike Zabrocki_, Nov 10 2004
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