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Search: id:A000242
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| A000242 |
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3rd power of rooted tree enumerator; number of linear forests of 3 rooted trees.
(Formerly M2798 N1126)
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+0
5
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| 1, 3, 9, 25, 69, 186, 503, 1353, 3651, 9865, 26748, 72729, 198447, 543159, 1491402, 4107152, 11342826, 31408719, 87189987, 242603970, 676524372, 1890436117, 5292722721, 14845095153, 41708679697, 117372283086, 330795842217
(list; graph; listen)
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OFFSET
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3,2
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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. 150.
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LINKS
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T. D. Noe, Table of n, a(n) for n=3..200
Index entries for sequences related to rooted trees
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FORMULA
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G.f.: B(x)^3 where B(x) is g.f. of 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, x=0, n+1), x, n): seq (a(n), n=3..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
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CROSSREFS
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Cf. A000081, A000106, A000300, A000343, A000395.
Sequence in context: A085327 A069403 A094292 this_sequence A077846 A005322 A103780
Adjacent sequences: A000239 A000240 A000241 this_sequence A000243 A000244 A000245
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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 from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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