%I A047874
%S A047874 1,1,1,1,4,1,1,13,9,1,1,41,61,16,1,1,131,381,181,25,1,1,428,2332,
%T A047874 1821,421,36,1,1,1429,14337,17557,6105,841,49,1,1,4861,89497,167449,
%U A047874 83029,16465,1513,64,1,1,16795,569794,1604098,1100902,296326,38281
%N A047874 Triangle of numbers T(n,k) = number of permutations of (1,2,...,n) with 
               longest increasing subsequence of length k (1<=k<=n).
%C A047874 Mirror image of triangle in A126065.
%D A047874 P. Diaconis, Group Representations in Probability and Statistics, IMS, 
               1988; see p. 112.
%D A047874 Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory 
               Ser. A 53 (1990), no. 2, 257-285.
%D A047874 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 A047874 Hunt, J. and Szymanski, T., "A fast algorithm for computing longest common 
               subsequences". Commun. ACM, 20 (1977), 350-353.
%D A047874 Schensted, C., "Longest increasing and decreasing subsequences". Canadian 
               J. Math. 13 (1961), 179-191.
%H A047874 Wikipedia, <a href="http://en.wikipedia.org/wiki/Longest_increasing_subsequence_problem">
               Longest increasing subsequence problem</a>
%e A047874 1; 1 1; 1 4 1; 1 13 9 1; 1 41 61 16 1; ...
%e A047874 T(3,2)=4 because 132, 213, 231, 312 have longest increasing subsequences 
               of length 2.
%Y A047874 Cf. A047887 and A047888. Rows give A001453, A001454, A001455, A001456, 
               A001457, A001458.
%Y A047874 Sequence in context: A158815 A101275 A039755 this_sequence A080248 A139382 
               A157180
%Y A047874 Adjacent sequences: A047871 A047872 A047873 this_sequence A047875 A047876 
               A047877
%K A047874 nonn,easy,nice,tabl
%O A047874 1,5
%A A047874 Eric Rains (rains(AT)caltech.edu)