A147746 Riordan array (1, x(1-2x)/(1-3x+x^2)).

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 5, 3, 1, 0, 13, 14, 9, 4, 1, 0, 34, 40, 28, 14, 5, 1, 0, 89, 114, 87, 48, 20, 6, 1, 0, 233, 323, 267, 161, 75, 27, 7, 1, 0, 610, 910, 809, 528, 270, 110, 35, 8, 1

Offset: 0

Author

Paul Barry, Nov 11 2008

Keywords

• easy
• nonn
• tabl

Comments

Triangle [0,1,1,1,0,0,0,....] DELTA [1,0,0,0,...] with Deléham DELTA as in A084938.

Note that 1/(1-x/(1-x/(1-x))) = (1-2x)/(1-3x+x^2). Row sums are A124302.

A147746*A007318 = A147747.

Examples

			Triangle begins
  1;
  0,   1;
  0,   1,   1;
  0,   2,   2,   1;
  0,   5,   5,   3,   1;
  0,  13,  14,   9,   4,   1;
  0,  34,  40,  28,  14,   5,   1;
  0,  89, 114,  87,  48,  20,   6,   1;
  ...
		

Programs

Mathematica

(* The function RiordanArray is defined in A256893. *)
RiordanArray[1&, # (1-2#)/(1-3#+#^2)&, 10] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

Formula

Sum_{k=0..n} T(n,k)*2^k = A147748(n). - Philippe Deléham, Oct 30 2011

Sum_{k=0..n} T(n,k)*(-1)^(n-k) = A215936(n). - Philippe Deléham, Aug 30 2012

G.f.: (1 - 3*x + x^2)/(1 - 3*x + x^2 - x*y + 2*x^2*y). - R. J. Mathar, Aug 11 2015