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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
6
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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
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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.
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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.
Sequence in context: A036038 A078760 A103280 this_sequence A035206 A115196 A093346
Adjacent sequences: A046896 A046897 A046898 this_sequence A046900 A046901 A046902
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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