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EXAMPLE
| If we form a table from the family of sequences defined by:
number of k-level labeled rooted trees with n leaves,
then this sequence equals the diagonal in that table:
n=1:A000012=[1,1,1,1,1,1,1,1,1,1,...];
n=2:A000110=[1,2,5,15,52,203,877,4140,21147,115975,...];
n=3:A000258=[1,3,12,60,358,2471,19302,167894,1606137,...];
n=4:A000307=[1,4,22,154,1304,12915,146115,1855570,26097835,...];
n=5:A000357=[1,5,35,315,3455,44590,660665,11035095,204904830,...];
n=6:A000405=[1,6,51,561,7556,120196,2201856,45592666,1051951026,...];
n=7:A001669=[1,7,70,910,14532,274778,5995892,148154860,4085619622,...];
n=8:A081624=[1,8,92,1380,25488,558426,14140722,406005804,13024655442,...];
n=9:A081629=[1,9,117,1989,41709,1038975,29947185,979687005,35839643175,..].
Row n in the above table equals column 0 of matrix power A008277^n
where A008277 = triangle of Stirling numbers of 2nd kind:
1;
1,1;
1,3,1;
1,7,6,1;
1,15,25,10,1;
1,31,90,65,15,1; ...
The name of this sequence is a generalization of the definition given
in the above sequences by Christian G. Bower (bowerc(AT)usa.net).
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