A338397 Triangle read by rows: T(n,m)= Sum_{k=0..m/2} C(n-k,m-2*k)*C(n-k,m-k)*C(n,k)/C(2*k,k).

1, 1, 1, 1, 4, 2, 1, 9, 12, 4, 1, 16, 42, 34, 8, 1, 25, 110, 160, 90, 16, 1, 36, 240, 550, 540, 226, 32, 1, 49, 462, 1540, 2310, 1666, 546, 64, 1, 64, 812, 3724, 7910, 8596, 4802, 1282, 128, 1, 81, 1332, 8064, 23058, 34986, 29190, 13140, 2946, 256

Offset: 0

Author

Vladimir Kruchinin, Oct 23 2020

Keywords

• nonn
• tabl

Examples

			1,
1, 1,
1, 4, 2,
1, 9, 12, 4,
1, 16, 42, 34, 8,
1, 25, 110, 160, 90, 16,
1, 36, 240, 550, 540, 226, 32
		

Crossrefs

Cf. A001263, A008459, A176280 (row sums), A338372.

Programs

Maxima

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

Formula

G.f.: A008459(x,y)/(1-(x*y*A008459(x,y))^2).