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A162717
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A partial-sum Narayana product
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0
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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
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OFFSET
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0,5
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COMMENTS
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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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LINKS
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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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KEYWORD
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AUTHOR
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STATUS
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approved
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