A119329 Number triangle T(n,k)=sum{j=0..n-k, C(k,2j)C(n-k,2j)*2^j}.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 13, 19, 13, 1, 1, 1, 1, 21, 37, 37, 21, 1, 1, 1, 1, 31, 61, 77, 61, 31, 1, 1, 1, 1, 43, 91, 141, 141, 91, 43, 1, 1, 1, 1, 57, 127, 241, 301, 241, 127, 57, 1, 1

Offset

0,13

Comments

Row sums are A119330. Product of Pascal's triangle A007318 and A119331. T(n,k)=T(n,n-k).

Links

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

Formula

Column k has g.f. (x^k/(1-x))*sum{j=0..k, C(k,2j)*2^j*(x/(1-x))^(2j)}

Example

Triangle begins
1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 1, 3, 1, 1,
1, 1, 7, 7, 1, 1,
1, 1, 13, 19, 13, 1, 1,
1, 1, 21, 37, 37, 21, 1, 1

Crossrefs

Cf. A119326.

Sequence in context: A058663 A124371 A147989 * A334549 A333901 A054724

Adjacent sequences: A119326 A119327 A119328 * A119330 A119331 A119332

Keyword

easy,nonn,tabl

Author

Paul Barry, May 14 2006

Status

approved