%I A047889
%S A047889 1,1,2,6,24,119,694,4582,33324,261808,2190688,19318688,178108704,
%T A047889 1705985883,16891621166,172188608886,1801013405436,19274897768196,
%U A047889 210573149141896,2343553478425816,26525044132374656,304856947930144656
%N A047889 Number of permutations in S_n with longest increasing subsequence of 
               length <= 4.
%C A047889 Also, the dimension of the space of SL(4)-invariants in V^m \otimes (V^*)^m, 
               where V is the standard 4-dimensional representation of SL(4) and 
               V^* its dual. - Alec Mihailovs (alec(AT)mihailovs.com), Aug 14 2005
%D A047889 Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory 
               Ser. A 53 (1990), no. 2, 257-285.
%H A047889 F. Bergeron and F. Gascon, <a href="http://www.cs.uwaterloo.ca/journals/
               JIS/index.html">Counting Young tableaux of bounded height</a>, J. 
               Integer Sequences, Vol. 3 (2000), #00.1.7.
%H A047889 <a href="Sindx_Y.html#Young">Index entries for sequences related to Young 
               tableaux.</a>
%F A047889 a(0)=1, a(1)=1, (n^3+16*n^2+85*n+150)*a(n+2) = (20*n^3+182*n^2+510*n+428)*a(n+1)-(64*n^3+256*n^2+320*n+128)*a\
               (n) - Alec Mihailovs (alec(AT)mihailovs.com), Aug 14 2005
%p A047889 A:=rsolve({a(0) = 1, a(1) = 1, (n^3 + 16*n^2 + 85*n + 150)*a(n + 2) = 
               > (20*n^3 + 182*n^2 + 510*n + 428)*a(n + 1) - (64*n^3 + 256*n^2 + 
               320*n +128)*a(n)}, a(n), makeproc): - Alec Mihailovs (alec(AT)mihailovs.com), 
               Aug 14 2005
%Y A047889 A column of A047888. Cf. A005802, A047890, A052399.
%Y A047889 Sequence in context: A005394 A095818 A052397 this_sequence A094198 A071077 
               A005395
%Y A047889 Adjacent sequences: A047886 A047887 A047888 this_sequence A047890 A047891 
               A047892
%K A047889 nonn,easy
%O A047889 0,3
%A A047889 Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane (njas(AT)research.att.com).
%E A047889 More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 01 2002
%E A047889 Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008 at 
               the suggestion of R. J. Mathar