cp's OEIS Frontend

A001457 Number of permutations of length n with longest increasing subsequence of length 6.

%I A001457 M5256 N2288 #40 Oct 27 2023 19:12:11
%S A001457 1,36,841,16465,296326,5122877,87116283,1477363967,25191909848,
%T A001457 434119587475,7583461369373,134533482045389,2426299018270338,
%U A001457 44506885647682026,830512607486659272,15764082963927084216,304295666452406076997,5971518739677370493811
%N A001457 Number of permutations of length n with longest increasing subsequence of length 6.
%C A001457 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 A001457 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 A001457 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001457 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001457 Vaclav Kotesovec, <a href="/A001457/b001457.txt">Table of n, a(n) for n = 6..175</a> (first 100 terms from Alois P. Heinz)
%H A001457 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 A001457 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 A001457 a(n) ~ 5 * 2^(2*n+6) * 3^(2*n+21) / (Pi^(5/2) * n^(35/2)). - _Vaclav Kotesovec_, Mar 18 2014
%Y A001457 Column k=6 of A047874.
%K A001457 nonn
%O A001457 6,2
%A A001457 _N. J. A. Sloane_
%E A001457 More terms from _Alois P. Heinz_, Jul 01 2012
%E A001457 Name of the sequence clarified by _Vaclav Kotesovec_, Mar 18 2014