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A332910 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

%I A332910 #5 Mar 02 2020 11:38:47
%S A332910 1,43,785,14065,234646,3890624,65790726,1149152226,20755593249,
%T A332910 389723127653,7616467493381,155034653456005,3285524611730078,
%U A332910 72467273447829602,1661985062849397148,39610017536621076924,979981089604037392299,25145506663601266049403
%N A332910 Number of entries in the sixth cycles of all permutations of [n] when cycles are ordered by increasing lengths.
%H A332910 Alois P. Heinz, <a href="/A332910/b332910.txt">Table of n, a(n) for n = 6..450</a>
%H A332910 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332910 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332910 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332910       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332910         b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]
%p A332910          (n, i$j, n-i*j)), j=0..n/i)))
%p A332910     end:
%p A332910 a:= n-> b(n, 1, 6)[2]:
%p A332910 seq(a(n), n=6..23);
%Y A332910 Column k=6 of A322383.
%K A332910 nonn
%O A332910 6,2
%A A332910 _Alois P. Heinz_, Mar 02 2020