A001457 Number of permutations of length n with longest increasing subsequence of length 6. (Formerly M5256 N2288)

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

Offset

6,2

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.

Formula

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

Crossrefs

Column k=6 of A047874.

Sequence in context: A028163 A054622 A028108 * A203271 A004360 A238931

Adjacent sequences: A001454 A001455 A001456 * A001458 A001459 A001460

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Jul 01 2012

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

Status

approved