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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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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; refs; listen; history; internal format)
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OFFSET
| 3,2
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.
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
| 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
| G.f.: B(x)^3 where B(x) is g.f. of A000081.
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MAPLE
| 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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MATHEMATICA
| max = 29; b[n_] := b[n] = If[n <= 1, n, Sum[k*b[k]*s[n-1, k], {k, 1, n-1}]/(n-1)]; s[n_, k_] := s[n, k] = Sum[ b[n+1-j*k], {j, 1, Quotient[n, k]}]; f[x_] := Sum[ b[k]*x^k, {k, 0, max}]; Drop[ CoefficientList[ Series[f[x]^3, {x, 0, max}], x], 3] (* From Jean-François Alcover, Oct 25 2011, after Alois P. Heinz *)
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CROSSREFS
| Cf. A000081, A000106, A000300, A000343, A000395.
Sequence in context: A069403 A094292 A201533 * A077846 A005322 A103780
Adjacent sequences: A000239 A000240 A000241 * A000243 A000244 A000245
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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