A099745 - OEIS

%I #5 Feb 14 2017 12:38:13

%S 0,0,0,0,12,168,1409,9187,51362,258674,1207855,5326205,22459080,

%T 91368900,360977373,1391835607,5257593566,19515948358,71358739003,

%U 257521313441,918732810340,3244576312440,11355547678665,39423281302875,135876498446042,465248862099418

%N Number of permutations of [n] with exactly 2 valleys which avoid the permutation 1324.

%H Colin Barker, <a href="/A099745/b099745.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (20,-174,860,-2641,5160,-6264,4320,-1296).

%F G.f.: x^5*(12-72*x+137*x^2-81*x^3) / ((1-3*x)^4*(1-2*x)^4).

%F a(n) = (162*(-239*2^n+80*3^(1+n)) - (9909*2^n+6128*3^n)*n - 24*(27*2^n-2*3^n)*n^2 + (27*2^n+32*3^n)*n^3) / 2592. - _Colin Barker_, Feb 14 2017

%o (PARI) concat(vector(4), Vec(x^5*(12-72*x+137*x^2-81*x^3) / ((1-3*x)^4*(1-2*x)^4) + O(x^30))) \\ _Colin Barker_, Feb 14 2017

%Y Cf. A000079.

%K nonn,easy

%O 1,5

%A _Mike Zabrocki_, Nov 09 2004