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A000526
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Partially labeled trees with n nodes (5 of which are labeled).
(Formerly M5387 N2340)
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8
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125, 1296, 8716, 47787, 232154, 1040014, 4395772, 17781210, 69498964, 264248924, 982218072, 3582421612, 12857819052, 45515994861, 159205157535, 551049504784, 1889714853263, 6427147635062, 21698583468717
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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5,1
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.
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
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Table of n, a(n) for n=5..23.
Index entries for sequences related to trees
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FORMULA
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G.f.: A(x) = B(x)^5*(125-204*B(x)+118*B(x)^2-24*B(x)^3)/(1-B(x))^7, 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-4)^5* (125-204*B(n-4) +118*B(n-4)^2 -24*B(n-4)^3)/ (1-B(n-4))^7, x=0, n+1), x, n): seq (a(n), n=5..23); [From Alois P. Heinz, Aug 21 2008]
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CROSSREFS
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Cf. A000055, A000107, A000243, A000269, A000444, A000485, A000524, A000525.
Sequence in context: A088896 A016851 A204795 * A016971 A030082 A017043
Adjacent sequences: A000523 A000524 A000525 * A000527 A000528 A000529
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Vladeta Jovovic, Oct 19 2001
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STATUS
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approved
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