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Search: id:A111125
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| A111125 |
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Triangle read by rows: T(k,s) = ((2k+1)/(2s+1))*binomial(k+s,2s), 0 <= s <= k. |
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+0
9
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| 1, 3, 1, 5, 5, 1, 7, 14, 7, 1, 9, 30, 27, 9, 1, 11, 55, 77, 44, 11, 1, 13, 91, 182, 156, 65, 13, 1, 15, 140, 378, 450, 275, 90, 15, 1, 17, 204, 714, 1122, 935, 442, 119, 17, 1, 19, 285, 1254, 2508, 2717, 1729, 665, 152, 19, 1, 21, 385, 2079, 5148, 7007, 5733, 2940, 952
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Riordan array ((1+x)/(1-x)^2,x/(1-x)^2). Row sums are A002878. Diagonal sums are A003945. Inverse is A113187. An interesting factorization is (1/(1-x),x/(1-x))(1+2x,x(1+x)). - Paul Barry (pbarry(AT)wit.ie), Oct 17 2005
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REFERENCES
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K. Dilcher and K. B. Stolarsky, A Pascal-type triangle characterizing twin primes, Amer. Math. Monthly, 112 (2005), 673-681.
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EXAMPLE
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Triangle begins:
1
3 1
5 5 1
7 14 7 1
9 30 27 9 1
11 55 77 44 11 1
13 91 182 156 65 13 1
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CROSSREFS
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Mirror image of A082985, which see for further references, etc.
Also closely related to triangles in A098599 and A100218.
Sequence in context: A131768 A084533 A082985 this_sequence A072919 A104489 A067285
Adjacent sequences: A111122 A111123 A111124 this_sequence A111126 A111127 A111128
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 16 2005
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EXTENSIONS
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More terms from Paul Barry (pbarry(AT)wit.ie), Oct 17 2005
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