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A346319 Number of permutations of [n] having four 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 A346319 #5 Jul 13 2021 17:18:03
%S A346319 1,10,85,665,5033,37632,280760,2100560,15799344,119598336,911432704,
%T A346319 6991479040,53960703232,418803056640,3266623490048,25590201536512,
%U A346319 201220024528896,1587256170708992,12553933544030208,99511621823561728,790240133265817600,6284788112052715520
%N A346319 Number of permutations of [n] having four 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 A346319 Alois P. Heinz, <a href="/A346319/b346319.txt">Table of n, a(n) for n = 4..1000</a>
%H A346319 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (40,-700,7056,-45360,194304,-561728,1082624,-1332224,946176,-294912).
%F A346319 G.f.: (18432*x^10 -68352*x^9 +115136*x^8 -117072*x^7 +80628*x^6 -38652*x^5 +12733*x^4 -2791*x^3 +385*x^2 -30*x+1)*x^4 / ((8*x-1) *(6*x-1)^2 *(4*x-1)^3 *(2*x-1)^4).
%Y A346319 Column k=4 of A344855.
%K A346319 nonn,easy
%O A346319 4,2
%A A346319 _Alois P. Heinz_, Jul 13 2021