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A101489
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Square array T(n,k), read by antidiagonals: number of binary trees, with n nodes that have no label greater than k.
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1
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1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 4, 1, 1, 2, 5, 10, 10, 1, 1, 2, 5, 13, 26, 26, 1, 1, 2, 5, 14, 37, 73, 73, 1, 1, 2, 5, 14, 41, 109, 213, 213, 1, 1, 2, 5, 14, 42, 126, 334, 645, 645, 1, 1, 2, 5, 14, 42, 131, 398, 1050, 2007, 2007, 1, 1, 2, 5, 14, 42, 132, 422, 1289, 3377
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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LINKS
| M. Bousquet-Melou, Limit laws for embedded trees
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FORMULA
| G.f. of k-th row: A(t)=B(t)*(1-C(t)^(k+2))*(1-C(t)^(k+7))/[(1-C(t)^(k+4))*(1-C(t)^(k+5))], with B(t) the g.f. of A000108 and C(t) the g.f. of A101490.
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EXAMPLE
| 1,1,1,2,4,10,26,73,213,645,
1,1,2,4,10,26,73,213,645,2007,
1,1,2,5,13,37,109,334,1050,3377,
1,1,2,5,14,41,126,398,1289,4253,
1,1,2,5,14,42,131,422,1390,4664,
1,1,2,5,14,42,132,428,1422,4812,
1,1,2,5,14,42,132,429,1429,4853,
1,1,2,5,14,42,132,429,1430,4861,
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CROSSREFS
| Rows converge to A000108. First row is A101488.
Sequence in context: A059260 A135229 A081372 * A104156 A070166 A131373
Adjacent sequences: A101486 A101487 A101488 * A101490 A101491 A101492
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, Jan 21 2005
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