A155887 Riordan array (1, (1/(1-x))c(x/(1-x))), c(x) the g.f. of A000108.

1, 0, 1, 0, 2, 1, 0, 5, 4, 1, 0, 15, 14, 6, 1, 0, 51, 50, 27, 8, 1, 0, 188, 187, 113, 44, 10, 1, 0, 731, 730, 468, 212, 65, 12, 1, 0, 2950, 2949, 1956, 970, 355, 90, 14, 1, 0, 12235, 12234, 8291, 4356, 1785, 550, 119, 16, 1, 0, 51822, 51821, 35643, 19474, 8612, 3021

Offset: 0

Author

Paul Barry, Jan 29 2009

Keywords

• easy
• nonn
• tabl

Comments

Inverse of (1, x(1-x)/(1+x-x^2)). Row sums are A002212. Augmented version of A104259.

Triangle T(n,k) given by [0,F(3)/F(1),F(1)/F(3),F(5)/F(3),F(3)/F(5),F(7)/F(5),F(5)/F(7),...] DELTA [1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938, F(n)=A000045(n) (Fibonacci numbers). - Philippe Deléham, Jan 31 2009

Examples

			Triangle begins
  1;
  0,    1;
  0,    2,    1;
  0,    5,    4,    1;
  0,   15,   14,    6,   1;
  0,   51,   50,   27,   8,   1;
  0,  188,  187,  113,  44,  10,  1;
  0,  731,  730,  468, 212,  65, 12,  1;
  0, 2950, 2949, 1956, 970, 355, 90, 14, 1;
From _Paul Barry_, Sep 28 2009: (Start)
Production matrix is
  0, 1,
  0, 2, 1,
  0, 1, 2, 1,
  0, 1, 1, 2, 1,
  0, 1, 1, 1, 2, 1,
  0, 1, 1, 1, 1, 2, 1,
  0, 1, 1, 1, 1, 1, 2, 1,
  0, 1, 1, 1, 1, 1, 1, 2, 1,
  0, 1, 1, 1, 1, 1, 1, 1, 2, 1 (End)
		

Formula

Riordan array (1, (1-sqrt((1-5x)/(1-x)))/(2x));

G.f.: 1/(1-xy/(1-x-x/(1-x/(1-x-x/(1-x/(1-x-x/(1-... (continued fraction).