A239432 Number of permutations of length n with longest increasing subsequence of length 8.

1, 64, 2521, 79861, 2250887, 59367101, 1508071384, 37558353900, 927716186325, 22904111472825, 568209449266202, 14216730315766814, 359666061054003144, 9216708503647774264, 239524408949706575548, 6317740398995612513164, 169207499997274346326579, 4602911809939402715164066

Offset: 8

Author

Vaclav Kotesovec, Mar 18 2014

Keywords

• nonn

Comments

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].

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 8..135
• A. Regev, Asymptotic values for degrees associated with strips of Young diagrams, Adv. in Math. 41 (1981), 115-136.

Crossrefs

Cf. A047874, A001453, A001454, A001455, A001456, A001457, A001458.

Formula

a(n) ~ 1913625 * 2^(6*n+77) / (Pi^(7/2) * n^(63/2)).