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A000106
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2nd power of rooted tree enumerator; number of linear forests of 2 rooted trees.
(Formerly M1415 N0553)
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8
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1, 2, 5, 12, 30, 74, 188, 478, 1235, 3214, 8450, 22370, 59676, 160140, 432237, 1172436, 3194870, 8741442, 24007045, 66154654, 182864692, 506909562, 1408854940, 3925075510, 10959698606, 30665337738, 85967279447
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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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=2..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 385
Index entries for sequences related to rooted trees
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FORMULA
| Self-convolution of rooted trees 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-1)^2, x=0, n+1), x, n): seq (a(n), n=2..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
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MATHEMATICA
| <<NumericalDifferentialEquationAnalysis`; btc = ButcherTreeCount[max = 30]; Flatten[ Table[ ListConvolve[t=Take[btc, n], t], {n, 1, max}]] (* From Jean-François Alcover, Nov 02 2011 *)
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CROSSREFS
| Cf. A000081, A000242, A000300, A000343, A000395.
Sequence in context: A118649 A033482 A054341 * A076883 A140832 A026580
Adjacent sequences: A000103 A000104 A000105 * A000107 A000108 A000109
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KEYWORD
| nonn,nice,easy
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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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