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A143911
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Triangle read by rows: T(n,k) = number of forests on n labeled nodes, where k is the maximum of the number of edges per tree (n>=1, 0<=k<=n-1).
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1
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1, 1, 1, 1, 3, 3, 1, 9, 12, 16, 1, 25, 60, 80, 125, 1, 75, 330, 480, 750, 1296, 1, 231, 1680, 3920, 5250, 9072, 16807, 1, 763, 9408, 33600, 49000, 72576, 134456, 262144, 1, 2619, 56952, 254016, 598500, 762048, 1210104, 2359296, 4782969, 1, 9495, 348120
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1035
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FORMULA
| See program.
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EXAMPLE
| T(4,1) = 9, because 9 forests on 4 labeled nodes have 1 as the maximum of the number of edges per tree:
.1-2. .1.2. .1.2. .1.2. .1.2. .1.2. .1-2. .1.2. .1.2.
..... ...|. ..... .|... ..\.. ../.. ..... .|.|. ..X..
.4.3. .4.3. .4-3. .4.3. .4.3. .4.3. .4-3. .4.3. .4.3.
Triangle begins:
1
1, 1
1, 3, 3
1, 9, 12, 16
1, 25, 60, 80, 125
1, 75, 330, 480, 750, 1296
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MAPLE
| A:= (n, k)-> coeff (series (exp (sum (j^(j-2) *x^j/j!, j=1..k)), x, n+1), x, n)*n!: T:= (n, k)-> A(n, k+1)-A(n, k): seq (seq (T(n, k), k=0..n-1), n=1..11);
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CROSSREFS
| Row sums give A001858. Rightmost diagonal gives A000272. Column k=1 gives A001189. Cf. A138464.
Sequence in context: A122919 A188513 A157401 * A185422 A131889 A174287
Adjacent sequences: A143908 A143909 A143910 * A143912 A143913 A143914
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KEYWORD
| nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 04 2008
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