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A332856 Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

%I A332856 #4 Mar 02 2020 09:48:51
%S A332856 1,29,583,10366,177299,3029643,52724894,944353801,17510885251,
%T A332856 337239557401,6756438503137,140893616636126,3057901614671778,
%U A332856 69040616816923804,1620394508763080044,39500148841295346478,999160362731046844470,26200784568622019301658
%N A332856 Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
%H A332856 Alois P. Heinz, <a href="/A332856/b332856.txt">Table of n, a(n) for n = 7..450</a>
%H A332856 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332856 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332856 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A332856       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332856         b(n-i*j, min(n-i*j, i-1), max(0, t-j))/j!*
%p A332856         combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332856     end:
%p A332856 a:= n-> b(n$2, 7)[2]:
%p A332856 seq(a(n), n=7..24);
%Y A332856 Column k=7 of A322384.
%K A332856 nonn
%O A332856 7,2
%A A332856 _Alois P. Heinz_, Feb 26 2020