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A000554
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Number of labeled trees of diameter 3 with n nodes.
(Formerly M4843 N2070)
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1
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12, 60, 210, 630, 1736, 4536, 11430, 28050, 67452, 159588, 372554, 859950, 1965840, 4456176, 10026702, 22412970, 49806980, 110100060, 242220594, 530578950, 1157627352, 2516581800, 5452594550, 11777604930, 25367149836, 54492396756
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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REFERENCES
| J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to trees
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FORMULA
| a(n) = n(n-1)*S2(n-2, 2) where S2(n, k) denotes the Stirling numbers of 2nd kind -Victor Adamchik (adamchik(AT)cs.cmu.edu), Jul 19 2001
a(n) = n(n-1) * 2^(n-3) = 2*A000217(n-1)*A000225(n-3) - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2007
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MATHEMATICA
| f[n_] := n (n - 1)*StirlingS2[n - 2, 2]; Table[ f@n, {n, 4, 29}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2007
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CROSSREFS
| Sequence in context: A174642 A061624 A004302 * A012289 A012583 A009049
Adjacent sequences: A000551 A000552 A000553 * A000555 A000556 A000557
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2007
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