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Search: id:A144150
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| A144150 |
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where the g.f. of column k is 1+g^(k+1)(x) with g = x->exp(x)-1. |
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+0
2
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 5, 1, 1, 1, 4, 12, 15, 1, 1, 1, 5, 22, 60, 52, 1, 1, 1, 6, 35, 154, 358, 203, 1, 1, 1, 7, 51, 315, 1304, 2471, 877, 1, 1, 1, 8, 70, 561, 3455, 12915, 19302, 4140, 1, 1, 1, 9, 92, 910, 7556, 44590, 146115, 167894, 21147, 1, 1, 1, 10, 117
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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A(n,k) is also the number of (k+1)-level labeled rooted trees with n leaves.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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G.f. of column k: 1+g^(k+1)(x) with g = x->e^x-1.
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EXAMPLE
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Square array begins:
1 1 1 1 1 1 ...
1 1 1 1 1 1 ...
1 2 3 4 5 6 ...
1 5 12 22 35 51 ...
1 15 60 154 315 561 ...
1 52 358 1304 3455 7556 ...
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MAPLE
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g:= proc(p) local b; b:=proc(n) option remember; if n=0 then 1 else (n-1)! *add (p(k)*b(n-k)/ (k-1)!/ (n-k)!, k=1..n) fi end end: A:= (n, k)-> (g@@k)(1)(n): seq (seq(A(n, d-n), n=0..d), d=0..12);
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CROSSREFS
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Columns 0-10 give: A000012, A000110, A000258, A000307, A000357, A000405, A001669, A081624, A081629, A081697, A081740. Rows 0+1, 2-4give: A000012, A000027, A000326, A005945. Cf. A000142.
Sequence in context: A099555 A124530 A070914 this_sequence A124560 A112707 A054252
Adjacent sequences: A144147 A144148 A144149 this_sequence A144151 A144152 A144153
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 11 2008
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