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%I #8 Mar 26 2016 09:01:06
%S 1,64,2521,79861,2250887,59367101,1508071384,37558353900,927716186325,
%T 22904111472825,568209449266202,14216730315766814,359666061054003144,
%U 9216708503647774264,239524408949706575548,6317740398995612513164,169207499997274346326579,4602911809939402715164066
%N Number of permutations of length n with longest increasing subsequence of length 8.
%C In general, for column k of A047874 is a(n) ~ product(j!, j=0..k-1) * k^(2*n+k^2/2) / (2^((k-1)*(k+2)/2) * Pi^((k-1)/2) * n^((k^2-1)/2)) [Regev, 1981].
%H Vaclav Kotesovec, <a href="/A239432/b239432.txt">Table of n, a(n) for n = 8..135</a>
%H A. Regev, <a href="http://dx.doi.org/10.1016/0001-8708(81)90012-8">Asymptotic values for degrees associated with strips of Young diagrams</a>, Adv. in Math. 41 (1981), 115-136.
%F a(n) ~ 1913625 * 2^(6*n+77) / (Pi^(7/2) * n^(63/2)).
%Y Cf. A047874, A001453, A001454, A001455, A001456, A001457, A001458.
%K nonn
%O 8,2
%A _Vaclav Kotesovec_, Mar 18 2014
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