A001457 Number of permutations of length n with longest increasing subsequence of length 6.

1, 36, 841, 16465, 296326, 5122877, 87116283, 1477363967, 25191909848, 434119587475, 7583461369373, 134533482045389, 2426299018270338, 44506885647682026, 830512607486659272, 15764082963927084216, 304295666452406076997, 5971518739677370493811

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn

Comments

In general, for column k of A047874 is a_k(n) ~ (Product_{j=0..k-1} j!) * k^(2*n + k^2/2) / (2^((k-1)*(k+2)/2) * Pi^((k-1)/2) * n^((k^2-1)/2)) [Regev, 1981]. - Vaclav Kotesovec, Mar 18 2014

References

• J. M. Hammersley, A few seedings of research, in Proc. Sixth Berkeley Sympos. Math. Stat. and Prob., ed. L. M. le Cam et al., Univ. Calif. Press, 1972, Vol. I, pp. 345-394.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 6..175 (first 100 terms from Alois P. Heinz)
• R. M. Baer and P. Brock, Natural sorting over permutation spaces, Math. Comp. 22 1968 385-410.
• A. Regev, Asymptotic values for degrees associated with strips of Young diagrams, Adv. in Math. 41 (1981), 115-136.

Crossrefs

Column k=6 of A047874.

Formula

a(n) ~ 5 * 2^(2*n+6) * 3^(2*n+21) / (Pi^(5/2) * n^(35/2)). - Vaclav Kotesovec, Mar 18 2014

Extensions

More terms from Alois P. Heinz, Jul 01 2012

Name of the sequence clarified by Vaclav Kotesovec, Mar 18 2014