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A052843
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A simple grammar.
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1
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1, 1, 2, 3, 6, 10, 20, 38, 79, 162, 348, 751, 1661, 3695, 8335, 18919, 43310, 99664, 230700, 536327, 1252298, 2934508, 6900046, 16272771, 38484608, 91243851, 216839820, 516423974, 1232376315, 2946354649, 7056335478, 16926813939, 40665822366, 97836595223, 235697108115, 568531616730
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of forests of rooted unlabeled identity trees. Euler transform of A004111. - Geoffrey Critzer, Oct 13 2012
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REFERENCES
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F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 64, Eq. (3.3.15); p. 80, Problem 3.10.
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LINKS
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FORMULA
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MAPLE
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spec := [S, {C=Prod(Z, B), B=PowerSet(C), S=Set(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
# second Maple program:
with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(d*
b(d)*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*b(d),
d=divisors(j)) *a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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nn=35; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2k, 0, -s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i]s[n-1, i]i, {i, 1, n-1}]/(n-1); it=Table[a[i], {i, 1, nn}]; CoefficientList[Series[Product[1/(1-x^i)^it[[i]], {i, 1, nn}], {x, 0, nn}], x] (* after code given by Robert A. Russell in A004111 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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