A257532 Triangle, read by rows, T(n,k)=k/n*Sum_{i=0..n-k} C(2*n,n-k-i)*C(2*n+i-1,i).

1, 4, 1, 24, 8, 1, 172, 64, 12, 1, 1360, 536, 120, 16, 1, 11444, 4672, 1156, 192, 20, 1, 100520, 42024, 11088, 2096, 280, 24, 1, 911068, 387456, 106908, 22016, 3420, 384, 28, 1, 8457504, 3643448, 1038984, 227408, 39120, 5192, 504, 32, 1

Offset: 1

Author

Vladimir Kruchinin, Apr 28 2015

Keywords

• nonn
• tabl

Examples

			1;
4, 1;
24, 8, 1;
172, 64, 12, 1;
1360, 536, 120, 16, 1;
		

Crossrefs

Cf. A027307. First column = A032349.

Programs

Maxima

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

Formula

G.f.: 1/(1-x*B(x)^2*y)-1, where B(x) is g.f. of A027307.

G.f. satisfies A(x)=x*[(1+A(x))/(1-A(x))]^2.