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A162717
A partial-sum Narayana product
0
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
OFFSET
0,5
COMMENTS
Row sums are A014137 (partial sums of Catalan numbers).
Equal to product of Riordan array (1/(1-x),x) and Narayana triangle A090181.
FORMULA
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).
EXAMPLE
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
CROSSREFS
Cf. A104711.
Sequence in context: A098447 A202784 A175105 * A122175 A073165 A137153
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jul 11 2009
STATUS
approved