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A q-Catalan triangle for q=2.
1

%I #9 Sep 08 2013 19:59:24

%S 1,1,1,3,4,1,17,25,9,1,171,258,102,16,1,3113,4635,1788,290,25,1,

%T 106419,154048,54909,7910,665,36,1,7035649,9907933,3232971,385669,

%U 26257,1323,49,1,915028347,1262093470,382948336,37703584,1889650,71596,2380,64,1

%N A q-Catalan triangle for q=2.

%C First column is A015083. Row sums are A154828.

%F Triangle [1,2,4,8,16,32,...] DELTA [1,0,1,0,1,0,1,....] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Nov 28 2011

%F G.f.: 1/(1-(x+xy)/(1-2x/(1-(4x+xy)/(1-8x/(1-(16x+xy)/(1-.... (continued fraction).

%e Triangle begins

%e 1,

%e 1, 1,

%e 3, 4, 1,

%e 17, 25, 9, 1,

%e 171, 258, 102, 16, 1,

%e 3113, 4635, 1788, 290, 25, 1

%Y Cf. A060693.

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Jan 15 2009