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A036249
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Number of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)
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14
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0, 1, 2, 5, 13, 37, 108, 332, 1042, 3360, 11019, 36722, 123875, 422449, 1453553, 5040816, 17599468, 61814275, 218252584, 774226549, 2758043727, 9862357697, 35387662266, 127374191687, 459783039109, 1664042970924, 6037070913558, 21951214425140, 79981665585029
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f. satisfies: A(x) = x*exp( Sum_{n>=1} (A(x^n) + x^n)/n ). - Paul D. Hanna, Oct 19 2005
G.f.: (x/(1 - x)) * Product_{n>=1} 1/(1 - x^n)^a(n). - Ilya Gutkovskiy, Jun 28 2021
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*
add(d*a(d), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+b(n-1)) end:
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MATHEMATICA
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max = 27; A[_] = 1; Do[A[x_] = x*Exp[Sum[(A[x^k] + x^k)/k + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[A[x] + O[x]^max, x] (* Jean-François Alcover, May 25 2018 *)
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PROG
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(PARI) {a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x*exp(sum(m=1, n, (subst(A, x, x^m)+x^m)/m))); polcoeff(A, n, x)} \\ Paul D. Hanna, Oct 19 2005
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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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