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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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4
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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; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| A(n,k) is also the number of (k+1)-level labeled rooted trees with n leaves.
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REFERENCES
| E. T. Bell, The Iterated Exponential Integers, Annals of Mathematics, 39 (1938), 539-557.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..5049
Index entries for sequences related to rooted trees
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FORMULA
| G.f. of column k: 1 + g^(k+1)(x) with g = x->e^x-1.
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EXAMPLE
| 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
| 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
| Cf. A111672. Columns 0-10 give: A000012, A000110, A000258, A000307, A000357, A000405, A001669, A081624, A081629, A081697, A081740. Rows 0+1, 2-4 give: A000012, A000027, A000326, A005945. Cf. A000142.
Sequence in context: A099555 A124530 A070914 * A124560 A201949 A112707
Adjacent sequences: A144147 A144148 A144149 * A144151 A144152 A144153
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KEYWORD
| nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 11 2008
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