A001458 Number of permutations of length n with longest increasing subsequence of length 7.

1, 49, 1513, 38281, 874886, 18943343, 399080475, 8312317976, 172912977525, 3615907795025, 76340522760097, 1631788075873114, 35378058306185002, 778860477345867008, 17423197016288134608, 396169070839236609236, 9157097111888617643722, 215143361542096212159897

Offset: 7

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 = 7..150 (first 75 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=7 of A047874.

Formula

a(n) ~ 6075 * 7^(2*n+49/2) / (32768 * Pi^3 * n^24). - 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