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EXAMPLE
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Triangle begins:
1;
0,1;
0,0,2;
0,0,1,5;
0,0,0,10,14;
0,0,0,8,70,42;
0,0,0,4,160,424,132;
0,0,0,1,250,1978,2382,429;
0,0,0,0,302,6276,19508,12804,1430;
0,0,0,0,298,15674,106492,168608,66946,4862;
0,0,0,0,244,33148,451948,1445208,1337684,343772,16796;
0,0,0,0,162,61806,1614906,9459090,16974314,10003422,1744314,58786;
0,0,0,0,84,103932,5090124,51436848,161380816,180308420,71692452,8780912,208012; ...
1;
1, 1;
1, 2, 2, 1;
1, 3, 6, 9, 10, 8, 4, 1;
1, 4, 12, 30, 64, 118, 188, 258, 302, 298, 244, 162, 84, 32, 8, 1;
1, 5, 20, 70, 220, 630, 1656, 4014, 8994, 18654, 35832, 63750,...;
1, 6, 30, 135, 560, 2170, 7916, 27326, 89582, 279622, 832680,...;
where row n gives the g.f. of the n-th self-composition of (x+x^2).
ROW-REVERSAL yields triangle A158830:
1;
1, 0;
2, 0, 0;
5, 1, 0, 0;
14, 10, 0, 0, 0;
42, 70, 8, 0, 0, 0;
132, 424, 160, 4, 0, 0, 0;
429, 2382, 1978, 250, 1, 0, 0, 0; ...
where
g.f. of row n of A158825 = n-th iteration of x*Catalan(x).
1,1,2,5,14,42,132,429,1430,4862,16796,58786,...;
1,2,6,21,80,322,1348,5814,25674,115566,528528,...;
1,3,12,54,260,1310,6824,36478,199094,1105478,...;
1,4,20,110,640,3870,24084,153306,993978,...;
1,5,30,195,1330,9380,67844,500619,3755156,...;
1,6,42,315,2464,19852,163576,1372196,11682348,...;
1,7,56,476,4200,38052,351792,3305484,31478628,...;
1,8,72,684,6720,67620,693048,7209036,75915708,...; ...
which consists of successive iterations of x*Catalan(x).
(End)
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