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Search: id:A046899
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| A046899 |
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Triangle in which n-th row is {C(n+k,k), k=0..n}, n >= 0. |
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+0
9
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| 1, 1, 2, 1, 3, 6, 1, 4, 10, 20, 1, 5, 15, 35, 70, 1, 6, 21, 56, 126, 252, 1, 7, 28, 84, 210, 462, 924, 1, 8, 36, 120, 330, 792, 1716, 3432, 1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 1, 11, 66, 286, 1001
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums = A134391: (1, 3, 10, 35, 126, 362, 1726,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
T(n, k) is also the number of order-preserving full transformations (of an n- chain) of waist k (waist(alpha) = max(Im(alpha))). [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]
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REFERENCES
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H. W. Gould, A class of binomial sums and a series transformation, Utilitas Math., 45 (1994), 71-83.
Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving partial transformations. Journal of Algebra 278 (2004), 342-359. [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]
Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving full transformations. Semigroup Forum 72 (2006), 51-62. [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]
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EXAMPLE
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1
1, 2
1, 3, 6
1, 4, 10, 20
1, 5, 15, 35, 70
1, 6, 21, 56, 126, 252
1, 7, 28, 84, 210, 462, 924
1, 8, 36, 120, 330, 792, 1716, 3432
1, 9, 45, 165, 495, 1287, 3003, 6435, 12870
1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620
1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756
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MAPLE
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for n from 0 to 10 do seq( binomial(n+m, n), m = 0 .. n) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 09 2007
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CROSSREFS
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Cf. A046900, A134391.
Adjacent sequences: A046896 A046897 A046898 this_sequence A046900 A046901 A046902
Sequence in context: A036038 A078760 A103280 this_sequence A035206 A115196 A093346
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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