A306226 Triangle read by rows: T(n,k) = Sum_{i=0..n/2} C(n-i,i)*C(n-i,k-i)*C(n-1,i) (0 <= k <= n).

1, 1, 1, 1, 3, 2, 1, 7, 11, 5, 1, 13, 36, 37, 13, 1, 21, 92, 160, 123, 35, 1, 31, 200, 520, 655, 401, 96, 1, 43, 387, 1405, 2575, 2541, 1293, 267, 1, 57, 686, 3325, 8295, 11711, 9492, 4131, 750, 1, 73, 1136, 7112, 23128, 43736, 50148, 34476, 13107, 2123, 1, 91, 1782, 14040, 57708, 140112, 212856, 205332, 122535, 41353, 6046

Offset: 0

Author

Vladimir Kruchinin, Feb 16 2019

Keywords

• nonn
• tabl

Examples

			1;
1, 1;
1, 3, 2;
1, 7, 11, 5;
1, 13, 36, 37, 13;
1, 21, 92, 160, 123, 35;
		

Crossrefs

Cf. A123160.

Cf. A005773 (right diagonal).

Programs

Maxima

T(n,k):=sum(binomial(n-i,i)*binomial(n-i,k-i)*binomial(n-1,i),i,0,n/2);

Formula

G.f.: (x*y+x+1)/(2*sqrt((-x*y-x+1)^2-4*x*y*(x*y+x)))+1/2.