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A332855 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

%I A332855 #4 Mar 02 2020 09:30:32
%S A332855 1,22,351,5119,73639,1079354,16379573,259470719,4307274362,
%T A332855 75030122026,1371391459821,26279686081517,527342512678490,
%U A332855 11066063071281662,242501869570679674,5541839758896671994,131891449988832738324,3264575304106660189788,83932189324072639925142
%N A332855 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
%H A332855 Alois P. Heinz, <a href="/A332855/b332855.txt">Table of n, a(n) for n = 6..450</a>
%H A332855 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332855 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332855 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A332855       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332855         b(n-i*j, min(n-i*j, i-1), max(0, t-j))/j!*
%p A332855         combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332855     end:
%p A332855 a:= n-> b(n$2, 6)[2]:
%p A332855 seq(a(n), n=6..24);
%Y A332855 Column k=6 of A322384.
%K A332855 nonn
%O A332855 6,2
%A A332855 _Alois P. Heinz_, Feb 26 2020