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A007152
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Evolutionary trees of magnitude n.
(Formerly M3628)
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2
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1, 1, 4, 28, 301, 4466, 84974, 1974904, 54233540, 1718280152, 61695193880, 2475688513024, 109797950475448, 5333253012414224, 281576039542538368, 16055279332196218624, 983264280857581866112, 64369946360185677026048, 4485859513184032011682304, 331558482325457407154881024
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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REFERENCES
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L. R. Foulds and R. W. Robinson, Counting certain classes of evolutionary trees with singleton labels, Congress. Num., 44 (1984), 65-88.
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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MAPLE
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Q := proc(n)
option remember ;
if n <= 1 then
0;
else
%/2 ;
end if;
end proc:
if n = 1 then
1;
else
end if ;
end proc:
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MATHEMATICA
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m = 20;
A007151 = Rest[Range[0, m]! CoefficientList[ InverseSeries[ Series[(2x - E^x + 1)/(x + 1), {x, 0, m}], x], x]];
Q[n_] := Q[n] = If[n <= 1, 0, (1/2)(-A007151[[n - 1]] + A007151[[n]] + (n - 1) Q[n - 1])];
a[n_] := If[n == 1, 1, A007151[[n - 1]] + Q[n - 1]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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