A213600 - OEIS

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A213600

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

1

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

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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.

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