A162717 A partial-sum Narayana product

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.

Links

Table of n, a(n) for n=0..65.

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

Adjacent sequences: A162714 A162715 A162716 * A162718 A162719 A162720

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 11 2009

Status

approved