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A332911 Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by increasing lengths.

%I A332911 #5 Mar 02 2020 11:47:28
%S A332911 1,57,1297,28006,555446,10718940,207593322,4101787080,83030091003,
%T A332911 1731086543933,37278557659029,830606719626674,19158608403920978,
%U A332911 457571632376980948,11312327413794558348,289427158238453113152,7659193100381954895675,209516361790095291013179
%N A332911 Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by increasing lengths.
%H A332911 Alois P. Heinz, <a href="/A332911/b332911.txt">Table of n, a(n) for n = 7..450</a>
%H A332911 Andrew V. Sills, <a href="https://arxiv.org/abs/1912.05306">Integer Partitions Probability Distributions</a>, arXiv:1912.05306 [math.CO], 2019.
%H A332911 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A332911 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332911       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
%p A332911         b(n-i*j, i+1, max(0, t-j))/j!*combinat[multinomial]
%p A332911          (n, i$j, n-i*j)), j=0..n/i)))
%p A332911     end:
%p A332911 a:= n-> b(n, 1, 7)[2]:
%p A332911 seq(a(n), n=7..24);
%Y A332911 Column k=7 of A322383.
%K A332911 nonn
%O A332911 7,2
%A A332911 _Alois P. Heinz_, Mar 02 2020