A213600 Triangle T(n,k) read by rows: Number of Dyck n-paths with midpoint at height k.

1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 4, 0, 9, 0, 1, 0, 25, 0, 16, 0, 1, 25, 0, 81, 0, 25, 0, 1, 0, 196, 0, 196, 0, 36, 0, 1, 196, 0, 784, 0, 400, 0, 49, 0, 1, 0, 1764, 0, 2304, 0, 729, 0, 64, 0, 1, 1764, 0, 8100, 0, 5625, 0, 1225, 0, 81, 0, 1, 0, 17424, 0, 27225, 0, 12100, 0

Offset

0,8

Links

Table of n, a(n) for n=0..72.

Formula

T(n,k) = A053121(n,k)^2.

Example

Triangle T(n,k) begins:
     1
     0    1
     1    0    1
     0    4    0    1
     4    0    9    0    1
     0   25    0   16    0   1
    25    0   81    0   25   0    1
     0  196    0  196    0  36    0  1
   196    0  784    0  400   0   49  0  1
     0 1764    0 2304    0 729    0 64  0  1
  1764    0 8100    0 5625   0 1225  0 81  0  1
  ...

Crossrefs

Row sums give A000108.

T(2n,0) gives A001246.

T(2n,2) gives A338727(n) for n>=1.

Cf. A053121.

Sequence in context: A292143 A350824 A281441 * A178104 A172545 A124321

Adjacent sequences: A213597 A213598 A213599 * A213601 A213602 A213603

Keyword

nonn,tabl

Author

David Scambler, Jun 14 2012

Status

approved