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A055302
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Triangle of labeled rooted trees with n nodes and k leaves.
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13
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1, 2, 0, 6, 3, 0, 24, 36, 4, 0, 120, 360, 140, 5, 0, 720, 3600, 3000, 450, 6, 0, 5040, 37800, 54600, 18900, 1302, 7, 0, 40320, 423360, 940800, 588000, 101136, 3528, 8, 0, 362880, 5080320, 16087680, 15876000, 5143824, 486864, 9144, 9, 0, 3628800
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
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FORMULA
| E.g.f. (relative to x) satisfies A(x, y)=xy+x*exp(A(x, y))-x. Divides by n and shifts up under exponential transform.
T(n, k) = (n!/k!)*Stirling2(n-1, n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 28 2004
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EXAMPLE
| 1; 2,0; 6,3,0; 24,36,4,0; 120,360,140,5,0; ...
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CROSSREFS
| Row sums give A000169. Columns 1 through 12: A000142, A055303-A055313. Cf. A055314.
Sequence in context: A054877 A095834 A106828 * A055349 A161174 A136656
Adjacent sequences: A055299 A055300 A055301 * A055303 A055304 A055305
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KEYWORD
| nonn,tabl,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), May 11 2000
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