%I M5297 N2304 #41 Oct 27 2023 19:12:48

%S 1,49,1513,38281,874886,18943343,399080475,8312317976,172912977525,

%T 3615907795025,76340522760097,1631788075873114,35378058306185002,

%U 778860477345867008,17423197016288134608,396169070839236609236,9157097111888617643722,215143361542096212159897

%N Number of permutations of length n with longest increasing subsequence of length 7.

%C 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

%D 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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vaclav Kotesovec, <a href="/A001458/b001458.txt">Table of n, a(n) for n = 7..150</a> (first 75 terms from Alois P. Heinz)

%H R. M. Baer and P. Brock, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0228216-8">Natural sorting over permutation spaces</a>, Math. Comp. 22 1968 385-410.

%H A. Regev, <a href="http://dx.doi.org/10.1016/0001-8708(81)90012-8">Asymptotic values for degrees associated with strips of Young diagrams</a>, Adv. in Math. 41 (1981), 115-136.

%F a(n) ~ 6075 * 7^(2*n+49/2) / (32768 * Pi^3 * n^24). - _Vaclav Kotesovec_, Mar 18 2014

%Y Column k=7 of A047874.

%K nonn

%O 7,2

%A _N. J. A. Sloane_

%E More terms from _Alois P. Heinz_, Jul 01 2012

%E Name of the sequence clarified by _Vaclav Kotesovec_, Mar 18 2014