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%I #2 Mar 30 2012 18:59:22
%S 1,1,1,3,2,1,9,7,3,1,29,24,12,4,1,97,85,46,18,5,1,333,306,177,76,25,6,
%T 1,1165,1115,681,315,115,33,7,1,4135,4100,2622,1288,510,164,42,8,1,
%U 14845,15185,10104,5220,2206,774,224,52,9,1
%N Renewal array for 1/(x+sqrt(1-4x)).
%C First column is A081696. Row sums are A000984.
%C Contribution from _Paul Barry_, Jan 27 2009: (Start)
%C First column of A155788.
%C In general, the image of the sequence with g.f. 1/(1-ax-bx^2) under (1,xc(x)) has g.f.
%C 1/(1-ax-(a+b)x/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction). (End)
%F Riordan array (1/(x+sqrt(1-4x)),x/(x+sqrt(1-4x));
%F G.f.: 1/(1-x-xy-2x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction).
%F G.f: 1/(1-x-2x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-.... (continued fraction). [From _Paul Barry_, Jan 27 2009]
%e Triangle begins
%e 1,
%e 1, 1,
%e 3, 2, 1,
%e 9, 7, 3, 1,
%e 29, 24, 12, 4, 1,
%e 97, 85, 46, 18, 5, 1,
%e 333, 306, 177, 76, 25, 6, 1
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Jan 27 2009
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