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A006790
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Exponentiation of e.g.f. for trees A000055(n-1).
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1
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1, 2, 5, 15, 53, 211, 938, 4582, 24349, 139671, 858745, 5628789, 39145021, 287667582, 2226033629, 18082308403, 153770703339, 1365631349757, 12638233544989, 121640399661294, 1215438543434225, 12587691428792115
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OFFSET
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0,2
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LINKS
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MAPLE
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with(numtheory):
b:= proc(n) option remember; `if`(n<=1, n, add(add(d*
b(d), d=divisors(j))*b(n-j), j=1..n-1)/(n-1))
end:
t:= proc(n) option remember; `if`(n=0, 1, b(n)-(add(b(k)
*b(n-k), k=0..n)-`if`(irem(n, 2)=0, b(n/2), 0))/2)
end:
g:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, j-1) *t(j-1) *g(n-j), j=1..n))
end:
a:= n-> g(n+1):
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MATHEMATICA
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b[n_] := b[n] = If[n <= 1, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]; t[n_] := t[n] = If[n==0, 1, b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[ Mod[n, 2] == 0, b[n/2], 0])/2]; g[n_] := g[n] = If[n==0, 1, Sum[Binomial[n-1, j-1] *t[j-1]*g[n-j], {j, 1, n}]]; a[n_] := g[n+1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 30 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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