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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..37.

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

Formula

Riordan array (1/sqrt(1-8x),(1-4x-sqrt(1-8x)/(8x)); T(n,k)=2^(n-k)*A094527(n,k).

Example

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

Mathematica

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

Crossrefs

Cf. A128413.

Sequence in context: A337204 A166027 A158978 * A257532 A183875 A136232

Adjacent sequences: A128414 A128415 A128416 * A128418 A128419 A128420

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 02 2007

Status

approved