A119305 Riordan array (1-4x, x(1-x)^3).

1, -4, 1, 0, -7, 1, 0, 15, -10, 1, 0, -13, 39, -13, 1, 0, 4, -80, 72, -16, 1, 0, 0, 95, -228, 114, -19, 1, 0, 0, -66, 462, -484, 165, -22, 1, 0, 0, 25, -630, 1375, -875, 225, -25, 1, 0, 0, -4, 588, -2772, 3185, -1428, 294, -28, 1, 0, 0, 0, -372, 4092, -8463, 6324, -2170, 372

Offset: 0

Author

Paul Barry, May 13 2006

Keywords

• easy
• sign
• tabl

Comments

Inverse of number triangle binomial(4n-k, n-k), A119304. Row sums are A119306.

Examples

			Triangle begins
   1;
  -4,    1;
   0,   -7,    1;
   0,   15,  -10,    1;
   0,  -13,   39,  -13,    1;
   0,    4,  -80,   72,  -16,    1;
   0,    0,   95, -228,  114,  -19,    1;
		

Links

• Indranil Ghosh, Rows 0..101, flattened

Programs

Mathematica

Flatten[Table[(Binomial[3k,n-k]+4Binomial[3k,n-k-1])*(-1)^(n-k),{n,0,11},{k,0,n}]] (* Indranil Ghosh, Feb 26 2017 *)

PARI

tabl(nn) = {for (n=0,nn,for (k=0,n,print1((binomial(3*k,n-k)+4*binomial(3*k,n-k-1))*(-1)^(n-k),", "););print(););} \\ Indranil Ghosh, Feb 26 2017

Formula

Number triangle T(n,k) = (C(3k, n-k) + 4*C(3k, n-k-1))(-1)^(n-k).