A318397 Triangle read by rows: T(n,k) = binomial(n,k)^2 * binomial(2*(n-k), n-k).

1, 2, 1, 6, 8, 1, 20, 54, 18, 1, 70, 320, 216, 32, 1, 252, 1750, 2000, 600, 50, 1, 924, 9072, 15750, 8000, 1350, 72, 1, 3432, 45276, 111132, 85750, 24500, 2646, 98, 1, 12870, 219648, 724416, 790272, 343000, 62720, 4704, 128, 1, 48620, 1042470, 4447872, 6519744, 4000752, 1111320, 141120, 7776, 162, 1

Offset: 0

Author

Michael Somos, Aug 25 2018

Keywords

• nonn
• tabl
• easy

Comments

The square of the triangular matrix {binomial(n, k)^2}_{k=0..n} A008459 read by rows.

Examples

			Triangle begins:
   1
   2   1
   6   8   1
  20  54  18   1
  70 320 216  32   1
...
		

Crossrefs

Row sums give A002893.

Cf. A008459.

Programs

Mathematica

T[ n_, k_] := Binomial[n, k]^2 Binomial[2 n - 2 k, n - k];

PARI

{T(n, k) = binomial(n, k)^2 * binomial(2*(n-k), n-k)};