

A122908


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


0



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
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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)^(nj)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: A282133 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



