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A332857 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

%I A332857 #5 Mar 02 2020 07:37:04
%S A332857 1,37,916,19526,392085,7734663,153275513,3090075848,63852563521,
%T A332857 1358480574137,29837098126826,677555150712614,15919961048979164,
%U A332857 387124513859258764,9741441909198136488,253578333540120825224,6825015749404715358362,189819840262710177446426
%N A332857 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
%H A332857 Alois P. Heinz, <a href="/A332857/b332857.txt">Table of n, a(n) for n = 8..450</a>
%H A332857 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332857 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332857 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A332857       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332857         b(n-i*j, min(n-i*j, i-1), max(0, t-j))/j!*
%p A332857         combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332857     end:
%p A332857 a:= n-> b(n$2, 8)[2]:
%p A332857 seq(a(n), n=8..26);
%Y A332857 Column k=8 of A322384.
%K A332857 nonn
%O A332857 8,2
%A A332857 _Alois P. Heinz_, Feb 26 2020