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%I #11 Mar 02 2020 07:03:33
%S 1,56,1992,58566,1569387,40210458,1011778943,25407870031,643294838111,
%T 16530707226038,433032539982493,11597633757170403,318186179384754262,
%U 8953723541105483282,258628065642282683675,7671629851218367059371,233734404206144319940526
%N Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
%H Alois P. Heinz, <a href="/A332859/b332859.txt">Table of n, a(n) for n = 10..450</a>
%H Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p b:= proc(n, l) option remember; `if`(n=0, l[10], add((j-1)!*b(n-j,
%p sort([l[], j], `>`)[1..10])*binomial(n-1, j-1), j=1..n))
%p end:
%p a:= n-> b(n, [0$10]):
%p seq(a(n), n=10..27);
%t b[n_, l_] := b[n, l] = If[n == 0, l[[10]], Sum[(j-1)!*b[n-j, ReverseSort[ Append[l, j]][[1 ;; 10]]] Binomial[n - 1, j - 1], {j, 1, n}]];
%t a[n_] := b[n, Table[0, {10}]];
%t a /@ Range[10, 27] (* _Jean-François Alcover_, Mar 01 2020, after _Alois P. Heinz_ *)
%Y Column k=10 of A322384.
%K nonn
%O 10,2
%A _Alois P. Heinz_, Feb 26 2020
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