A332910 - OEIS

%I #5 Mar 02 2020 11:38:47

%S 1,43,785,14065,234646,3890624,65790726,1149152226,20755593249,

%T 389723127653,7616467493381,155034653456005,3285524611730078,

%U 72467273447829602,1661985062849397148,39610017536621076924,979981089604037392299,25145506663601266049403

%N Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

%H Alois P. Heinz, <a href="/A332910/b332910.txt">Table of n, a(n) for n = 6..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, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,

%p       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*

%p         b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]

%p          (n, i$j, n-i*j)), j=0..n/i)))

%p     end:

%p a:= n-> b(n, 1, 6)[2]:

%p seq(a(n), n=6..23);

%Y Column k=6 of A322383.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Mar 02 2020