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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_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
AUTHOR
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 March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)