%I #12 Oct 17 2015 08:36:24

%S 1,10,0,115,10,0,1666,139,0,0,30198,2570,0,0,0,665148,47878,904,0,0,0,

%T 17296851,1017174,20972,0,0,0,0

%N Triangle T(n,m) (read as T(1,1); T(2,1), T(2,2); T(3,1), T(3,2), T(3,3);) Number of distinct non-recursive Catalan Automorphisms whose minimum clause-representation requires examination of n nodes in total, divided into m non-default clauses.

%H A. Karttunen, <a href="/A089839/a089839.c.txt">C-program for computing the initial terms of this sequence</a>

%H A. Karttunen, <a href="/A089840/a089840p.txt">Prolog-program which illustrates the construction of non-recursive Catalan bijections with clause-representations</a>

%H A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a>

%e ...... Triangle............................ Row sums

%e ........1........................................1

%e .......10.......0...............................10

%e ......115......10...0..........................125 = 5^3

%e .....1666.....139...0....0....................1805 = 5*19^2

%e ....30198....2570...0....0...0...............32768 = 32^3 = 8^5

%e ...665148...47878...904..0...0...0..........713930

%e .17296851.1017174.20972..0...0...0...0....18334997

%e T(1,1)=1, as there is just one non-identity, non-recursive Catalan bijection with a single non-default clause opening a single node, namely A089840[1]=A069770.

%e T(2,1)=10, as there are the following non-recursive Catalan bijections (rows 2-11 of A089840): A072796, A089850, A089851, A089852, A089853, A089854, A072797, A089855, A089856, A089857, whose minimum clause-representation consists of a single non-default clause that opens two nodes.

%e T(3,2)=10, as there are the following non-recursive Catalan bijections (rows 12-21 of A089840): A074679, A089858, A073269, A089859, A089860, A074680, A089861, A073270, A089862, A089863, whose minimum clause-representation consists of a two non-default clauses with total 3 nodes opened.

%Y First column: A089833. Row sums: A089832. Row sums excluding the first column: A089834.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Dec 05 2003