A167749 Riordan array (1,xf(x)) where f(x) is the g.f. of A005169 (fountains of coins).

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 2, 3, 3, 1, 0, 3, 6, 6, 4, 1, 0, 5, 11, 13, 10, 5, 1, 0, 9, 20, 27, 24, 15, 6, 1, 0, 15, 38, 54, 55, 40, 21, 7, 1, 0, 26, 70, 109, 120, 100, 62, 28, 8, 1, 0, 45, 129, 216, 258, 236, 168, 91, 36, 9, 1, 0, 78, 238, 423, 544, 540, 426, 266, 128, 45, 10, 1

Offset: 0

Author

Paul Barry, Nov 10 2009

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A167750. Diagonal sums are A167751.

Examples

			Triangle begins
1,
0, 1,
0, 1, 1,
0, 1, 2, 1,
0, 2, 3, 3, 1,
0, 3, 6, 6, 4, 1,
0, 5, 11, 13, 10, 5, 1,
0, 9, 20, 27, 24, 15, 6, 1,
0, 15, 38, 54, 55, 40, 21, 7, 1,
0, 26, 70, 109, 120, 100, 62, 28, 8, 1,
0, 45, 129, 216, 258, 236, 168, 91, 36, 9, 1,
0, 78, 238, 423, 544, 540, 426, 266, 128, 45, 10, 1,
0, 135, 437, 824, 1127, 1205, 1035, 721, 402, 174, 55, 11, 1
		

Formula

G.f.: 1/(1-xy/(1-x/(1-x^2/(1-x^3/(1-x^4/(1-... (continued fraction).