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

Author

Paul Barry, May 14 2006

Keywords

• easy
• nonn
• tabl

Comments

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

Examples

			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.

Formula

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