A113955 Riordan array (1/((1-4x)c(x)),xc(x)/sqrt(1-4x)), c(x) the g.f. of A000108.

1, 3, 1, 11, 6, 1, 42, 30, 9, 1, 163, 140, 58, 12, 1, 638, 630, 325, 95, 15, 1, 2510, 2772, 1686, 624, 141, 18, 1, 9908, 12012, 8330, 3682, 1064, 196, 21, 1, 39203, 51480, 39796, 20264, 7050, 1672, 260, 24, 1, 155382, 218790, 185517, 106203, 42849, 12303, 2475

Offset

0,2

Comments

Columns include A032443,A002457,A018218,A038836. Row sums are A100192. Diagonal sums are A113956.

Links

Table of n, a(n) for n=0..51.

Formula

Riordan array ((1/(1-4x)+1/sqrt(1-4x))/2, (2x/((1-4x)+sqrt(1-4x)))); Number triangle T(n, k)=sum{j=0..n, C(j, j-k)C(2n, n-j)}.

T(n,k)=sum{j=0..n, C(2n,j)C(n-j,k)}; - Paul Barry, Apr 03 2006

Example

Triangle begins
1;
3, 1;
11, 6, 1;
42, 30, 9, 1;
163, 140, 58, 12, 1;
638, 630, 325, 95, 15, 1;

Crossrefs

Sequence in context: A027516 A092808 A343171 * A110165 A111965 A110440

Adjacent sequences: A113952 A113953 A113954 * A113956 A113957 A113958

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 09 2005

Status

approved