cp's OEIS Frontend

A098992 Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324.

%I A098992 #6 Oct 26 2017 07:47:58
%S A098992 0,0,1,11,55,190,526,1254,2682,5280,9735,17017,28457,45838,71500,
%T A098992 108460,160548,232560,330429,461415,634315,859694,1150138,1520530,
%U A098992 1988350,2574000,3301155,4197141,5293341,6625630,8234840,10167256,12475144,15217312,18459705
%N A098992 Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324.
%H A098992 Colin Barker, <a href="/A098992/b098992.txt">Table of n, a(n) for n = 1..1000</a>
%H A098992 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A098992 G.f.: x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8.
%F A098992 From _Colin Barker_, Oct 26 2017: (Start)
%F A098992 a(n) = (n*(-540 + 476*n + 469*n^2 - 490*n^3 + 70*n^4 + 14*n^5 + n^6)) / 5040.
%F A098992 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A098992 (End)
%o A098992 (PARI) concat(vector(2), Vec(x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8 + O(x^30))) \\ _Colin Barker_, Oct 26 2017
%Y A098992 Cf. A061552, A000292.
%K A098992 easy,nonn
%O A098992 1,4
%A A098992 _Mike Zabrocki_, Nov 05 2004