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A346321 Number of permutations of [n] having six 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 A346321 #7 Apr 18 2023 12:19:13
%S A346321 1,21,322,4284,52941,627627,7264499,82948008,940359420,10628025408,
%T A346321 120071145376,1358324810752,15403850755456,175232115148032,
%U A346321 2000450203866368,22922052379355136,263639657993643008,3043516686354636800,35260990780587196416,409914386080322027520
%N A346321 Number of permutations of [n] having six 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 A346321 Alois P. Heinz, <a href="/A346321/b346321.txt">Table of n, a(n) for n = 6..932</a>
%H A346321 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (112, -5880, 192416, -4402160, 74858880, -981976576, 10178341888, -84702207744, 571843371008, -3151736133632, 14222131077120, -52534235435008, 158334587600896, -386804516978688, 757761436024832, -1171275127980032, 1394246317768704, -1231344289972224, 758836566687744, -290924978503680, 52183852646400).
%p A346321 b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
%p A346321       *binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 7)
%p A346321     end:
%p A346321 a:= n-> coeff(b(n), x, 6):
%p A346321 seq(a(n), n=6..29);
%Y A346321 Column k=6 of A344855.
%K A346321 nonn,easy
%O A346321 6,2
%A A346321 _Alois P. Heinz_, Jul 13 2021