A122908 A central binomial scaling of the Riordan array (1+x,x) (A097806).

1, 1, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 0, 3, 6, 0, 0, 0, 0, 6, 10, 0, 0, 0, 0, 0, 10, 20, 0, 0, 0, 0, 0, 0, 20, 35, 0, 0, 0, 0, 0, 0, 0, 35, 70, 0, 0, 0, 0, 0, 0, 0, 0, 70, 126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 252

Offset

0,6

Comments

Row sums are A050168. Diagonal sums are A001045 doubled. Row sums of inverse are 1/C(2n,n) aerated. Applications to other sequences are obvious.

Links

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

Formula

Number triangle T(n,k)=C(k,floor(k/2))*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}

Example

Triangle begins
.1,
.1, 1,
.0, 1, 2,
.0, 0, 2, 3,
.0, 0, 0, 3, 6,
.0, 0, 0, 0, 6, 10,
.0, 0, 0, 0, 0, 10, 20,
.0, 0, 0, 0, 0, 0, 20, 35,
.0, 0, 0, 0, 0, 0, 0, 35, 70,
.0, 0, 0, 0, 0, 0, 0, 0, 70, 126,
.0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 252

Crossrefs

Sequence in context: A338819 A153869 A128541 * A296441 A091008 A111006

Adjacent sequences: A122905 A122906 A122907 * A122909 A122910 A122911

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 18 2006

Status

approved