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Search: id:A000444
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| A000444 |
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Partially labeled rooted trees with n nodes (3 of which are labeled).
(Formerly M4641 N1984)
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+0
12
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| 9, 64, 326, 1433, 5799, 22224, 81987, 293987, 1031298, 3555085, 12081775, 40576240, 134919788, 444805274, 1455645411, 4733022100, 15302145060, 49223709597, 157629612076, 502736717207, 1597541346522, 5059625685739
(list; graph; listen)
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OFFSET
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3,1
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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. 134.
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LINKS
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Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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G.f.: A(x) = B(x)^3*(9-8*B(x)+2*B(x)^2)/(1-B(x))^5, where B(x) is g.f. for rooted trees with n nodes, cf. A000081.
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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-2)^3*(9-8*B(n-2)+2*B(n-2)^2)/(1-B(n-2))^5, x=0, n+1), x, n): seq (a(n), n=3..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
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CROSSREFS
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Cf. A000081, A000107, A000243, A000269, A000485, A000524-A000526.
Cf. A042977.
Sequence in context: A099761 A092396 A018201 this_sequence A143631 A083328 A000846
Adjacent sequences: A000441 A000442 A000443 this_sequence A000445 A000446 A000447
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KEYWORD
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nonn
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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 from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001
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