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Search: id:A072590
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| A072590 |
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Table T(n,k) giving number of spanning trees in complete bipartite graph K(n,k), read by antidiagonals. |
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5
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| 1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 32, 81, 32, 1, 1, 80, 432, 432, 80, 1, 1, 192, 2025, 4096, 2025, 192, 1, 1, 448, 8748, 32000, 32000, 8748, 448, 1, 1, 1024, 35721, 221184, 390625, 221184, 35721, 1024, 1, 1, 2304, 139968, 1404928, 4050000, 4050000
(list; table; graph; listen)
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OFFSET
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1,5
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REFERENCES
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J. W. Moon, "Counting Labeled Trees".
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Exercise 5.66.
H. I. Scoins, The number of trees with nodes of alternate parity, Proc. Cambridge Philos. Soc. 58 (1962) 12-16.
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LINKS
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T. D. Noe, Antidiagonals d=1..50, flattened
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FORMULA
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T(n, k) = n^(k-1)*k^(n-1).
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EXAMPLE
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1; 1,1; 1,4,1; 1,12,12,1; 1,32,81,32,1; 1,80,432,432,80,1; ...
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PROGRAM
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(PARI) T(n, k)=if(n<1|k<1, 0, n^(k-1)*k^(n-1))
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CROSSREFS
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A068087(n)=T(n, n). Cf. A001787, A069996.
Sequence in context: A154372 A080416 A099759 this_sequence A111636 A146990 A051433
Adjacent sequences: A072587 A072588 A072589 this_sequence A072591 A072592 A072593
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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Michael Somos
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EXTENSIONS
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Scoins reference from DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 22 2003
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