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Search: id:A128710
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| A128710 |
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Triangle read by rows: T(n,k)=(k+2)*binom(n,k) (0<=k<=n). |
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+0
1
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| 2, 2, 3, 2, 6, 4, 2, 9, 12, 5, 2, 12, 24, 20, 6, 2, 15, 40, 50, 30, 7, 2, 18, 60, 100, 90, 42, 8, 2, 21, 84, 175, 210, 147, 56, 9, 2, 24, 112, 280, 420, 392, 224, 72, 10, 2, 27, 144, 420, 756, 882, 672, 324, 90, 11, 2, 30, 180, 600, 1260, 1764, 1680, 1080, 450, 110, 12, 2, 33
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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k*C(n-4,k-2) counts the permutations in S_n which have zero occurrences of the pattern 213 and one occurrence of the pattern 132 and k descents.
Sum of row n =(n+4)2^(n-1) (A045623).- by Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2007
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REFERENCES
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D. Hoek, Parvisa moenster i permutationer [Swedish], (2007).
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EXAMPLE
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Triangle starts:
2;
2,3;
2,6,4;
2,9,12,5;
2,12,24,20,6;
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MAPLE
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T:=(n, k)->(k+2)*binomial(n, k): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2007
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CROSSREFS
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Cf. A045623.
Sequence in context: A108499 A107753 A078224 this_sequence A095757 A094438 A015996
Adjacent sequences: A128707 A128708 A128709 this_sequence A128711 A128712 A128713
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KEYWORD
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nonn,tabl
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AUTHOR
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David Hoek (david.hok(AT)telia.com), Mar 23 2007
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2007
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