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EXAMPLE
| Triangle begins:
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,...;
1, 7, 42, 231, 1190, 5810, 27076, 121023, 520626, 2161158,...;
1, 8, 56, 364, 2240, 13188, 74760, 409836, 2179556, 11271436,...;
1, 9, 72, 540, 3864, 26628, 177744, 1153740, 7303164, 45179508,...;
1, 10, 90, 765, 6240, 49260, 378312, 2836548, 20817588,...; ...
Multiplying the g.f. of column k by (1-x)^k, k>=1, with leading zeros,
yields the g.f. of row k in the triangle A122890:
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; ...
in which the main diagonal is the Catalan numbers
and the row sums form the factorials.
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