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A047888
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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.
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6
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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, 513, 119, 24, 6, 2, 1, 1, 1430, 2761, 694, 120, 24, 6, 2, 1, 1, 4862, 15767, 4582, 719, 120, 24, 6, 2, 1, 1, 16796, 94359, 33324, 5003, 720, 120, 24, 6, 2, 1, 1, 58786, 586590
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| 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
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REFERENCES
| Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
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CROSSREFS
| Rows of the array are partial sums of A047874. Cf. A047887.
Sequence in context: A128604 A098885 A106270 * A128704 A075259 A169589
Adjacent sequences: A047885 A047886 A047887 * A047889 A047890 A047891
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KEYWORD
| nonn,easy,nice,tabl
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AUTHOR
| Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 01 2002
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