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A001458 Number of permutations of length n with longest increasing subsequence of length 7.
(Formerly M5297 N2304)
3
1, 49, 1513, 38281, 874886, 18943343, 399080475, 8312317976, 172912977525, 3615907795025, 76340522760097, 1631788075873114, 35378058306185002, 778860477345867008, 17423197016288134608, 396169070839236609236, 9157097111888617643722, 215143361542096212159897 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,2

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]. - 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

Alois P. Heinz and 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.

FORMULA

a(n) ~ 6075 * 7^(2*n+49/2) / (32768 * Pi^3 * n^24). - Vaclav Kotesovec, Mar 18 2014

CROSSREFS

Column k=7 of A047874.

Sequence in context: A012238 A036226 A032655 * A004374 A203500 A069327

Adjacent sequences:  A001455 A001456 A001457 * A001459 A001460 A001461

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

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Last modified January 22 19:01 EST 2019. Contains 319365 sequences. (Running on oeis4.)