%I #7 Oct 28 2021 06:27:48

%S 1,2,1,1,5,2,1,1,2,5,14,5,1,2,2,1,5,42,14,1,5,2,2,5,1,14,132,42,1,14,

%T 2,5,5,2,14,1,42,429,132,1,42,2,14,5,5,14,2,42,1,132,1430,429,1,132,2,

%U 42,5,14,14,5,42,2,132,1,429,4862,1430,1,429,2,132,5,42,14,14,42,5,132,2

%N Table read by rows: the Catalan number C(n) followed by pairs (C(n-1-j), C(j+1)), j=0 to n-2.

%C The table starts row n with A000108(n) = C(n) and then visualizes the convolution formula C(n) = sum_{j=0..n-1} C(j)*C(n-1-j) by listing some pairs of that structure in the same row.

%e Starting in row n=1 the table reads

%e 1;

%e 2,1,1;

%e 5,2,1,1,2;

%e 14,5,1,2,2,1,5;

%e 42,14,1,5,2,2,5,1,14;

%e 132,42,1,14,2,5,5,2,14,1,42;

%e The row n=3 represents 5=2*1+1*1+1*2, for example, where the middle term is not represented in the table.

%Y cf. A000108.

%K nonn,tabf,less

%O 1,2

%A _Juri-Stepan Gerasimov_, Jul 04 2009

%E Definition and comment rephrased by _R. J. Mathar_, Sep 16 2009