A106190 Triangle read by rows: T(n,k) = binomial(2(n-k),n-k)/(1-2(n-k)).

1, -2, 1, -2, -2, 1, -4, -2, -2, 1, -10, -4, -2, -2, 1, -28, -10, -4, -2, -2, 1, -84, -28, -10, -4, -2, -2, 1, -264, -84, -28, -10, -4, -2, -2, 1, -858, -264, -84, -28, -10, -4, -2, -2, 1, -2860, -858, -264, -84, -28, -10, -4, -2, -2, 1, -9724, -2860, -858, -264, -84, -28, -10, -4, -2, -2, 1, -33592, -9724, -2860, -858

Offset: 0

Author

Paul Barry, Apr 24 2005

Keywords

• easy
• sign
• tabl

Comments

Sequence array for expansion of sqrt(1-4x).

Row sums are A106191. Diagonal sums are A106192. Sequence array for A002420. Inverse of number triangle A106187.

Riordan array (sqrt(1-4x),x).

Examples

			Triangle begins
1;
-2,1;
-2,-2,1;
-4,-2,-2,1;
-10,-4,-2,-2,1;
-28,-10,-4,-2,-2,1;
		

Programs

Mathematica

T[n_, k_] := Binomial[2(n - k), n - k]/(1 - 2(n - k)); Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* Robert G. Wilson v, Apr 25 2005 *)

Extensions

More terms from Robert G. Wilson v, Apr 25 2005