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A001458
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Number of permutations of length n with longest increasing subsequence of length 7.
(Formerly M5297 N2304)
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3
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1, 49, 1513, 38281, 874886, 18943343, 399080475, 8312317976, 172912977525, 3615907795025, 76340522760097, 1631788075873114, 35378058306185002, 778860477345867008, 17423197016288134608, 396169070839236609236, 9157097111888617643722, 215143361542096212159897
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OFFSET
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7,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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FORMULA
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a(n) ~ 6075 * 7^(2*n+49/2) / (32768 * Pi^3 * n^24). - Vaclav Kotesovec, Mar 18 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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