A128417 Number triangle T(n,k) = 2^(n-k)*C(2*n,n-k).

1, 4, 1, 24, 8, 1, 160, 60, 12, 1, 1120, 448, 112, 16, 1, 8064, 3360, 960, 180, 20, 1, 59136, 25344, 7920, 1760, 264, 24, 1, 439296, 192192, 64064, 16016, 2912, 364, 28, 1, 3294720, 1464320, 512512, 139776, 29120, 4480, 480, 32, 1

Offset: 0

Author

Paul Barry, Mar 02 2007

Keywords

• easy
• nonn
• tabl

Comments

Inverse of A128414. Row sums are A128418. Diagonal sums are A128419.

Examples

			Triangle begins:
  1,
  4, 1,
  24, 8, 1,
  160, 60, 12, 1,
  1120, 448, 112, 16, 1,
  8064, 3360, 960, 180, 20, 1,
  59136, 25344, 7920, 1760, 264, 24, 1,
  439296, 192192, 64064, 16016, 2912, 364, 28, 1
  ...
		

Links

• Sheng-Liang Yang, Yan-Ni Dong, and Tian-Xiao He, Some matrix identities on colored Motzkin paths, Discrete Mathematics 340.12 (2017): 3081-3091.

Crossrefs

Cf. A128413.

Programs

Mathematica

Flatten[Table[2^(n-k) Binomial[2n,n-k],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Nov 02 2011 *)

Formula

Riordan array (1/sqrt(1-8*x),(1-4*x-sqrt(1-8*x))/(8*x)).

T(n,k) = 2^(n-k)*A094527(n,k).