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Search: id:A047889
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| A047889 |
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Number of permutations in S_n with longest increasing subsequence of length <= 4. |
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+0
8
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| 1, 1, 2, 6, 24, 119, 694, 4582, 33324, 261808, 2190688, 19318688, 178108704, 1705985883, 16891621166, 172188608886, 1801013405436, 19274897768196, 210573149141896, 2343553478425816, 26525044132374656, 304856947930144656
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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
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REFERENCES
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Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
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LINKS
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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.
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FORMULA
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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
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MAPLE
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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
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CROSSREFS
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A column of A047888. Cf. A005802, A047890, A052399.
Sequence in context: A005394 A095818 A052397 this_sequence A094198 A071077 A005395
Adjacent sequences: A047886 A047887 A047888 this_sequence A047890 A047891 A047892
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KEYWORD
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nonn,easy
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AUTHOR
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Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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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
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