%I
%S 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,
%T 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,
%U 129,216,258,236,168,91,36,9,1,0,78,238,423,544,540,426,266,128,45,10,1
%N Riordan array (1,xf(x)) where f(x) is the g.f. of A005169 (fountains of coins).
%C Row sums are A167750. Diagonal sums are A167751.
%F G.f.: 1/(1xy/(1x/(1x^2/(1x^3/(1x^4/(1... (continued fraction).
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, 1, 1,
%e 0, 1, 2, 1,
%e 0, 2, 3, 3, 1,
%e 0, 3, 6, 6, 4, 1,
%e 0, 5, 11, 13, 10, 5, 1,
%e 0, 9, 20, 27, 24, 15, 6, 1,
%e 0, 15, 38, 54, 55, 40, 21, 7, 1,
%e 0, 26, 70, 109, 120, 100, 62, 28, 8, 1,
%e 0, 45, 129, 216, 258, 236, 168, 91, 36, 9, 1,
%e 0, 78, 238, 423, 544, 540, 426, 266, 128, 45, 10, 1,
%e 0, 135, 437, 824, 1127, 1205, 1035, 721, 402, 174, 55, 11, 1
%K easy,nonn,tabl
%O 0,9
%A _Paul Barry_, Nov 10 2009
