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A055327
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Triangle of rooted identity trees with n nodes and k leaves.
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7
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1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 6, 5, 1, 9, 13, 2, 1, 12, 28, 11, 1, 16, 53, 40, 3, 1, 20, 91, 109, 26, 1, 25, 146, 254, 116, 6, 1, 30, 223, 524, 387, 61, 1, 36, 326, 998, 1068, 329, 12, 1, 42, 461, 1774, 2587, 1289, 145, 1, 49, 634, 2995, 5678, 4133, 911, 25, 1, 56
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Row lengths are 1,1,1,2,2,3,3,4,4,5,5,6,6,...
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LINKS
| N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
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FORMULA
| G.f. satisfies A(x, y)=xy+x*WEIGH(A(x, y))-x. Shifts up under WEIGH transform.
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EXAMPLE
| 1; 1; 1; 1,1; 1,2; 1,4,1; 1,6,5; 1,9,13,2; 1,12,28,11; ...
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CROSSREFS
| Row sums give A004111. Columns 2 through 8: A002620(n-2), A055328-A055333. Cf. A055334.
Sequence in context: A127625 A124844 A133934 * A105260 A099510 A137633
Adjacent sequences: A055324 A055325 A055326 * A055328 A055329 A055330
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KEYWORD
| nonn,tabf,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), May 12 2000
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