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A332912 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

%I A332912 #5 Mar 02 2020 12:02:18
%S A332912 1,73,2026,51866,1205832,26820444,590148378,13100356128,295439599773,
%T A332912 6807481609901,160887057723746,3910224803769926,97864814302511668,
%U A332912 2524228366327596948,67113790045849483056,1839604074821982820944,51976021537896649002555
%N A332912 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by increasing lengths.
%H A332912 Alois P. Heinz, <a href="/A332912/b332912.txt">Table of n, a(n) for n = 8..450</a>
%H A332912 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332912 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332912 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332912       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332912         b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]
%p A332912          (n, i$j, n-i*j)), j=0..n/i)))
%p A332912     end:
%p A332912 a:= n-> b(n, 1, 8)[2]:
%p A332912 seq(a(n), n=8..24);
%Y A332912 Column k=8 of A322383.
%K A332912 nonn
%O A332912 8,2
%A A332912 _Alois P. Heinz_, Mar 02 2020