%I A047888
%S A047888 1,1,1,1,2,1,1,5,2,1,1,14,6,2,1,1,42,23,6,2,1,1,132,103,24,6,2,1,1,429,
%T A047888 513,119,24,6,2,1,1,1430,2761,694,120,24,6,2,1,1,4862,15767,4582,719,
%U A047888 120,24,6,2,1,1,16796,94359,33324,5003,720,120,24,6,2,1,1,58786,586590
%N A047888 Rectangular array of numbers a(n,k) = number of permutations of n things 
               with longest increasing subsequence of length <=k (1<=k<=infinity), 
               read by antidiagonals.
%C A047888 Also a(n,k) is the dimension of the space of SL(k)-invariants in V^n 
               tensor (V^*)^n, where V is the standard k-dimensional representation 
               of SL(k) and V^* is its dual. - Alec Mihailovs (alec(AT)mihailovs.com), 
               Aug 14 2005
%D A047888 Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory 
               Ser. A 53 (1990), no. 2, 257-285.
%Y A047888 Rows of the array are partial sums of A047874. Cf. A047887.
%Y A047888 Sequence in context: A128604 A098885 A106270 this_sequence A128704 A075259 
               A003570
%Y A047888 Adjacent sequences: A047885 A047886 A047887 this_sequence A047889 A047890 
               A047891
%K A047888 nonn,easy,nice,tabl
%O A047888 1,5
%A A047888 Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane (njas(AT)research.att.com).
%E A047888 More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 01 2002