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A046899 Triangle in which n-th row is {C(n+k,k), k=0..n}, n >= 0. +0
6
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)
OFFSET

0,3

COMMENT

Row sums = A134391: (1, 3, 10, 35, 126, 362, 1726,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007

REFERENCES

H. W. Gould, A class of binomial sums and a series transformation, Utilitas Math., 45 (1994), 71-83.

EXAMPLE

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

MAPLE

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

CROSSREFS

Cf. A046900, A134391.

Sequence in context: A036038 A078760 A103280 this_sequence A035206 A115196 A093346

Adjacent sequences: A046896 A046897 A046898 this_sequence A046900 A046901 A046902

KEYWORD

nonn,tabl,easy,nice

AUTHOR

njas

EXTENSIONS

More terms from James A. Sellers (sellersj(AT)math.psu.edu)

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.


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