cp's OEIS Frontend

A332914 Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

%I A332914 #5 Mar 02 2020 12:28:15
%S A332914 1,111,4357,150801,4654469,134049203,3729595473,102656565841,
%T A332914 2828539643998,78576462334232,2212108223706338,63356175294304198,
%U A332914 1851016172004724086,55265191691761995338,1688128671403459821842,52796230233728968111746,1691419149055825399281421
%N A332914 Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by increasing lengths.
%H A332914 Alois P. Heinz, <a href="/A332914/b332914.txt">Table of n, a(n) for n = 10..450</a>
%H A332914 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332914 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332914 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332914       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332914         b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]
%p A332914          (n, i$j, n-i*j)), j=0..n/i)))
%p A332914     end:
%p A332914 a:= n-> b(n, 1, 10)[2]:
%p A332914 seq(a(n), n=10..26);
%Y A332914 Column k=10 of A322383.
%K A332914 nonn
%O A332914 10,2
%A A332914 _Alois P. Heinz_, Mar 02 2020