|
| |
|
|
A047889
|
|
Number of permutations in S_n with longest increasing subsequence of length <= 4.
|
|
8
| |
|
|
1, 1, 2, 6, 24, 119, 694, 4582, 33324, 261808, 2190688, 19318688, 178108704, 1705985883, 16891621166, 172188608886, 1801013405436, 19274897768196, 210573149141896, 2343553478425816, 26525044132374656, 304856947930144656
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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
|
|
|
REFERENCES
| Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
|
|
|
LINKS
| F. Bergeron and F. Gascon, Counting Young tableaux of bounded height, J. Integer Sequences, Vol. 3 (2000), #00.1.7.
Index entries for sequences related to Young tableaux.
|
|
|
FORMULA
| 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
A047889(n) = (64*(n+1)*(2*n^3+21*n^2+76*n+89)*A002895(n)-(8*n^4+104*n^3+526*n^2+1098*n+776)*A002895(n+1))/(3*(n+2)^3*(n+3)^3*(n+4)) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jun 02 2010]
|
|
|
MAPLE
| 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
|
|
|
CROSSREFS
| A column of A047888. Cf. A005802, A047890, A052399.
Sequence in context: A005394 A095818 A052397 * A094198 A071077 A202213
Adjacent sequences: A047886 A047887 A047888 * A047890 A047891 A047892
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 01 2002
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008 at the suggestion of R. J. Mathar
|
| |
|
|
