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A346322 Number of permutations of [n] having seven 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 A346322 #7 Apr 20 2023 12:39:39
%S A346322 1,28,546,9030,136521,1956570,27124955,368258891,4934711782,
%T A346322 65608599056,868543125632,11476719098208,151628071536832,
%U A346322 2005351952310016,26570735233245952,352902891363604736,4699994984738296320,62779734338836996096,841132871051793858560
%N A346322 Number of permutations of [n] having seven 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 A346322 Alois P. Heinz, <a href="/A346322/b346322.txt">Table of n, a(n) for n = 7..879</a>
%H A346322 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (168, -13440, 681632, -24615360, 673960320, -14545867776, 254017792512, -3655881782784, 43944394303488, -445483185094656, 3835837793820672, -28195256256282624, 177510573498728448, -958975703677403136, 4447744859322580992, -17695513525640822784, 60260448721418846208, -175010175041662877696, 431158568263920648192, -894423403170908602368, 1546792199062741319680, -2199976821097607725056, 2525948081813952921600, -2280501363206944456704, 1556924686713055346688, -754785240817587978240, 231325591660815974400, -33664847019245568000).
%p A346322 b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
%p A346322       *binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 8)
%p A346322     end:
%p A346322 a:= n-> coeff(b(n), x, 7):
%p A346322 seq(a(n), n=7..29);
%Y A346322 Column k=7 of A344855.
%K A346322 nonn,easy
%O A346322 7,2
%A A346322 _Alois P. Heinz_, Jul 13 2021