cp's OEIS Frontend

A212347 Sequence of coefficients of x^1 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x).

%I A212347 #35 Jun 27 2025 00:45:39
%S A212347 14,56,144,300,550,924,1456,2184,3150,4400,5984,7956,10374,13300,
%T A212347 16800,20944,25806,31464,38000,45500,54054,63756,74704,87000,100750,
%U A212347 116064,133056,151844,172550,195300,220224,247456,277134,309400,344400,382284,423206,467324,514800,565800,620494,679056,741664,808500,879750,955604
%N A212347 Sequence of coefficients of x^1 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x).
%H A212347 S. Kitaev, J. Remmel and M. Tiefenbruck, <a href="http://arxiv.org/abs/1201.6243">Marked mesh patterns in 132-avoiding permutations I</a>, arXiv preprint arXiv:1201.6243, 2012
%H A212347 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A212347 For n>=5, a(n)=(n^2-2n-8)(n^2-2n-3)/6   or   a(n)=(n-4)*A212346(n-1).
%F A212347 G.f.: -2*x^5*(2*x^2-7*x+7) / (x-1)^5. - _Colin Barker_, Jul 22 2013
%t A212347 QQ0[t, x] = (1 - (1-4*x*t)^(1/2)) / (2*x*t); QQ1[t, x] = 1/(1 - t*QQ0[t, x]); QQ2[t, x] = (1 + t*(QQ1[t, x] - QQ0[t, x]))/(1 - t*QQ0[t, x]); QQ3[t, x] = (1 + t*(QQ2[t, x] - QQ0[t, x] + t*(QQ1[t, x] - QQ0[t, x])))/(1 - t*QQ0[t, x]); QQ4[t, x] = (1 + t*(QQ3[t, x] - QQ0[t, x] + t*(QQ2[t, x] - QQ0[t, x]) + (2*t^2*(QQ1[t, x] - QQ0[t, x]))))/(1 - t*QQ0[t, x]); CoefficientList[Coefficient[Simplify[Series[QQ4[t, x], {t, 0, 35}]],x],t] (* _Robert Price_, Jun 04 2012 *)
%t A212347 Table[(n-4)*(n-3)*(n+1)*(n+2)/6, {n, 5, 50}] (* _Jean-François Alcover_, Sep 21 2017 *)
%K A212347 nonn,easy
%O A212347 5,1
%A A212347 _N. J. A. Sloane_, May 09 2012
%E A212347 a(10)-a(35) from _Robert Price_, Jun 02 2012