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A332913 Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by increasing lengths.

%I A332913 #5 Mar 02 2020 12:15:15
%S A332913 1,91,3026,90597,2439516,61989747,1538707458,38139479553,953072924061,
%T A332913 24163160247008,624376555920980,16498591390522978,446749936369626468,
%U A332913 12412653806246040786,354123558880901036688,10378353585187092249138,312512449355524805863371
%N A332913 Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by increasing lengths.
%H A332913 Alois P. Heinz, <a href="/A332913/b332913.txt">Table of n, a(n) for n = 9..450</a>
%H A332913 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332913 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332913 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332913       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332913         b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]
%p A332913          (n, i$j, n-i*j)), j=0..n/i)))
%p A332913     end:
%p A332913 a:= n-> b(n, 1, 9)[2]:
%p A332913 seq(a(n), n=9..25);
%Y A332913 Column k=9 of A322383.
%K A332913 nonn
%O A332913 9,2
%A A332913 _Alois P. Heinz_, Mar 02 2020