A332859 - OEIS

%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