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%I #17 May 20 2016 18:44:05
%S 1,0,1,0,0,2,0,0,0,5,0,0,0,0,14,0,0,0,0,0,42,0,0,0,0,0,0,132,0,0,0,0,
%T 0,0,0,429,0,0,0,0,0,0,0,0,1430,0,0,0,0,0,0,0,0,0,4862,0,0,0,0,0,0,0,
%U 0,0,0,16796,0,0,0,0,0,0,0,0,0,0,0,58786,0,0,0,0,0,0,0,0,0,0,0,0,208012
%N A000108(n) preceded by n zeros.
%C Triangle given by A000004 DELTA A000012 where DELTA is the operator defined in A084938. - _Philippe Deléham_, Jul 12 2007
%C T(n,k) is the number of Dyck paths of semilength n having exactly k U=(1,1) steps. - _Alois P. Heinz_, Jun 09 2014
%H Alois P. Heinz, <a href="/A131427/b131427.txt">Rows n = 0..140, flattened</a>
%F A000108(n) preceded by n zeros, as an infinite lower triangular matrix.
%e First few rows of the triangle are:
%e 1;
%e 0, 1;
%e 0, 0, 2;
%e 0, 0, 0, 5;
%e 0, 0, 0, 0, 14;
%e 0, 0, 0, 0, 0, 42;
%e ...
%p T:= (n, k)-> `if`(k<n, 0, binomial(2*n, n)/(n+1)):
%p seq(seq(T(n, k), k=0..n), n=0..15); # _Alois P. Heinz_, Jun 09 2014
%t T[n_, n_] := CatalanNumber[n]; T[_, _] = 0;
%t Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, May 20 2016 *)
%Y Cf. A131428, A131429, A000108, A243752.
%K nonn,tabl
%O 0,6
%A _Gary W. Adamson_, Jul 10 2007
%E More terms from _Philippe Deléham_, Oct 16 2008
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