cp's OEIS Frontend

A346318 Number of permutations of [n] having three cycles of the form (c1, c2, ..., c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.

%I A346318 #11 Jun 11 2024 15:43:47
%S A346318 1,6,35,195,1078,5992,33632,190800,1093664,6327552,36904192,216676096,
%T A346318 1279012352,7581628416,45086720000,268774576128,1605129183232,
%U A346318 9598558142464,57453899350016,344139257020416,2062361588793344,12363724057214976,74138363625472000
%N A346318 Number of permutations of [n] having three cycles of the form (c1, c2, ..., c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.
%H A346318 Alois P. Heinz, <a href="/A346318/b346318.txt">Table of n, a(n) for n = 3..1000</a>
%H A346318 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (20,-160,656,-1456,1664,-768).
%F A346318 G.f.: (96*x^6-256*x^5+298*x^4-201*x^3+75*x^2-14*x+1)*x^3 / ((6*x-1) *(4*x-1)^2 *(2*x-1)^3).
%F A346318 For n>3, a(n) = 2^(n-7)*3^(n-1) + (n-2)*2^(2*n-8) + (n^2 - 3*n + 1)*2^(n-7). - _Vaclav Kotesovec_, Jul 15 2021
%t A346318 Drop[CoefficientList[Series[(96x^6-256x^5+298x^4-201x^3+75x^2-14x+1)x^3/((6x-1)(4x-1)^2 (2x-1)^3),{x,0,30}],x],3] (* _Harvey P. Dale_, Jun 11 2024 *)
%Y A346318 Column k=3 of A344855.
%K A346318 nonn,easy
%O A346318 3,2
%A A346318 _Alois P. Heinz_, Jul 13 2021