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Search: id:A000243
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| A000243 |
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Number of trees with n nodes, 2 of which are labeled.
(Formerly M2803 N1128)
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+0
9
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| 1, 3, 9, 26, 75, 214, 612, 1747, 4995, 14294, 40967, 117560, 337830, 972027, 2800210, 8075889, 23315775, 67380458, 194901273, 564239262, 1634763697, 4739866803, 13752309730, 39926751310, 115988095896, 337138003197
(list; graph; listen)
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OFFSET
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2,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..200
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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a(n) = A000107(n)-A000081(n).
G.f.: A(x) = B(x)^2/(1-B(x)), where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001
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MAPLE
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b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add (b(k)*x^k, k=1..n) end: a:= n-> coeff (series (B(n-1)^2/(1-B(n-1)), x=0, n+1), x, n): seq (a(n), n=2..27); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
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CROSSREFS
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Cf. A000055, A000081, A000269, A000485, A000526, A000107, A000524, A000444, A000525.
Sequence in context: A127911 A116423 A077845 this_sequence A076264 A123941 A018919
Adjacent sequences: A000240 A000241 A000242 this_sequence A000244 A000245 A000246
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, new description and formula from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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