A144092 Triangle of Hankel transforms of sequence array of C(n,floor(n/2))

1, 1, 1, 1, 0, 1, 1, -1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 2, -4, 2, 1, 1, 0, 3, 0, 10, 0, 1, 1, -1, 3, 9, 15, -25, 5, 1, 1, 0, 4, 0, 42, 0, 70, 0, 1, 1, 1, 4, -16, 56, 196, 196, -196, 14, 1, 1, 0, 5, 0, 120, 0, 1176

Offset

0,13

Comments

The parity matrix A144093 of this array seems to have row sums A061338(n+1).

Links

Table of n, a(n) for n=0..61.

Formula

Triangle (-1)^C(k+1,2)*H(n,k) where the k-th column of H(n,k) is the Hankel transform of the k-th column of the array [k<=n]*C(n-k,floor((n-k)/2).

Example

Triangle begins
1,
1, 1,
1, 0, 1,
1, -1, 1, 1,
1, 0, 2, 0, 1,
1, 1, 2, -4, 2, 1,
1, 0, 3, 0, 10, 0, 1,
1, -1, 3, 9, 15, -25, 5, 1,
1, 0, 4, 0, 42, 0, 70, 0, 1,
1, 1, 4, -16, 56, 196, 196, -196, 14, 1,
1, 0, 5, 0, 120, 0, 1176, 0, 588, 0, 1

Crossrefs

Sequence in context: A121303 A166396 A152221 * A333467 A120648 A215401

Adjacent sequences: A144089 A144090 A144091 * A144093 A144094 A144095

Keyword

easy,sign,tabl

Author

Paul Barry, Sep 10 2008

Status

approved