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Search: id:A000343
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| A000343 |
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5th power of rooted tree enumerator; number of linear forests of 5 rooted trees.
(Formerly M3901 N1601)
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+0
5
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| 1, 5, 20, 70, 230, 721, 2200, 6575, 19385, 56575, 163952, 472645, 1357550, 3888820, 11119325, 31753269, 90603650, 258401245, 736796675, 2100818555, 5990757124, 17087376630, 48753542665, 139155765455, 397356692275
(list; graph; listen)
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OFFSET
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5,2
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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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Index entries for sequences related to rooted trees
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FORMULA
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G.f.: B(x)^5 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-4)^5, x=0, n+1), x, n): seq (a(n), n=5..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, A000242, A000300, A000395.
Sequence in context: A160549 A089094 A080930 this_sequence A005324 A154638 A054889
Adjacent sequences: A000340 A000341 A000342 this_sequence A000344 A000345 A000346
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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 Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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