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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
OFFSET
7,2
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 = 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.
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
KEYWORD
nonn
EXTENSIONS
More terms from Alois P. Heinz, Jul 01 2012
Name of the sequence clarified by Vaclav Kotesovec, Mar 18 2014
STATUS
approved