A348593 Triangle read by rows: T(n,m) = Sum_{j=0..min(m,n-m)} C(2j,j)*C(n-2j-1,m-j)*C(n-m,j)/(j+1).

1, 1, 1, 2, 1, 4, 1, 1, 6, 7, 1, 1, 8, 18, 6, 1, 1, 10, 34, 30, 7, 1, 1, 12, 55, 88, 33, 8, 1, 1, 14, 81, 195, 145, 42, 9, 1, 1, 16, 112, 366, 460, 184, 52, 10, 1, 1, 18, 148, 616, 1146, 763, 248, 63, 11, 1, 1, 20, 189, 960, 2422, 2544, 1060, 324, 75, 12, 1, 1, 22, 235, 1413, 4558, 6916, 4282, 1490, 413, 88, 13, 1

Offset: 0

Author

Vladimir Kruchinin, Jan 25 2022

Keywords

• nonn
• tabf

Examples

			Triangle begins
  1;
  1;
  1,  2;
  1,  4,  1;
  1,  6,  7,  1;
  1,  8, 18,  6,  1;
  1, 10, 34, 30,  7,  1;
  1, 12, 55, 88, 33,  8,  1;
		

Crossrefs

Row sums give A173992.

Cf. A000108, A307374.

Programs

Maxima

T(n,m):=sum(binomial(2*j,j)*binomial(n-2*j-1,m-j)*binomial(n-m,j)/(j+1), j,0,min(m,n-m));

Formula

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

Sum_{m>=0} (-1)^m * T(n,m) = A307374(n). - Alois P. Heinz, Jan 26 2022