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%I #20 Aug 12 2020 11:39:39
%S 0,0,0,0,0,0,0,1080,12960,143424,1641600,19915200,257644800,
%T 3556224000,52289556480,817133184000,13536585216000,237105792000000,
%U 4380335511552000,85148431867699200,1737742314147840000,37156364106301440000,830772012055265280000
%N Number of elements of S_n with strategic pile of size 6.
%C Strategic pile is as defined in A267323.
%C The formula given below is a specific instance of the formula that will appear in "Quantifying CDS Sortability of Permutations Using Strategic Piles", see link.
%H M. Gaetz, B. Molokach, M. Scheepers, and M. Shanks, <a href="https://math.boisestate.edu/reu/publications/quantifying-cds-sortability.pdf">Quantifying CDS Sortability of Permutations Using Strategic Piles</a>
%H Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks, <a href="https://arxiv.org/abs/1811.11937">Quantifying CDS Sortability of Permutations by Strategic Pile Size</a>, arXiv:1811.11937 [math.CO], 2018.
%F a(n) = (n-6)!*(120*binomial(n-7,5) + 576*binomial(n-7,4) + 1116*binomial(n-7,3) + 1080*binomial(n-7,2) + 540*binomial(n-7,1)) for n>7.
%e The permutation P = [3,5,1,8,6,2,7,4] has strategic pile of size 6. This can be found by the following cycle composition: (0,4,7,2,6,8,1,5,3)(0,1,2,3,4,5,6,7,8)=(0,5,8,4,3,7,1,6,2). Therefore, the strategic pile of P is {4,3,7,1,6,2}.
%Y Cf. A267323 (size 3), A267324 (size 4), A267391 (size 5).
%K nonn
%O 1,8
%A _Marisa Gaetz_, Jan 18 2017
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