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Search: id:A162717
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| A162717 |
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A partial-sum Narayana product |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 7, 1, 1, 5, 20, 27, 11, 1, 1, 6, 35, 77, 61, 16, 1, 1, 7, 56, 182, 236, 121, 22, 1, 1, 8, 84, 378, 726, 611, 218, 29, 1, 1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1, 1, 10, 165, 1254, 4422, 7667, 6686, 2885, 577, 46, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A014137 (partial sums of Catalan numbers).
Equal to product of Riordan array (1/(1-x),x) and Narayana triangle A090181.
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FORMULA
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Number triangle T(n,k)=sum{j=0..n, C(n,j)*if(k<=j, C(j-1,2j-2k)*A000108(j-k),0)}; G.f.: 1/(1-x-x(1-x)y/(1-x/(1-xy/(1-x/(1-xy/(1-... (continued fraction).
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EXAMPLE
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Triangle begins
1,
1, 1,
1, 2, 1,
1, 3, 4, 1,
1, 4, 10, 7, 1,
1, 5, 20, 27, 11, 1,
1, 6, 35, 77, 61, 16, 1,
1, 7, 56, 182, 236, 121, 22, 1,
1, 8, 84, 378, 726, 611, 218, 29, 1,
1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1
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CROSSREFS
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Cf. A104711.
Sequence in context: A144823 A098446 A098447 this_sequence A122175 A073165 A137153
Adjacent sequences: A162714 A162715 A162716 this_sequence A162718 A162719 A162720
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 11 2009
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