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A073075
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Generating function satisfies A(x) = exp(2*A(x)*x + 2*A(x^3)*x^3/3 + 2*A(x^5)*x^5/5 + 2*A(x^7)*x^7/7 +...).
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9
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1, 2, 6, 22, 86, 358, 1554, 6950, 31822, 148434, 702802, 3369046, 16319050, 79749294, 392711090, 1946732854, 9706813790, 48651303118, 244972282734, 1238621756174, 6286144819506, 32011282859598, 163517409895602, 837631563577814, 4301996341244810
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OFFSET
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0,2
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COMMENTS
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Which kind of trees is counted by this sequence (see formulas)? - Joerg Arndt, Mar 04 2015
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LINKS
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FORMULA
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G.f.: A(x) = exp(sum_{n>=0} 2*A(x^(2n+1))*x^(2n+1)/(2n+1)), A(0)=1, where A(x) = 1 + 2x + 6x^2 + 22x^3 + 86x^4 + 358x^5 +...
Let b(n) = a(n-1) for n>=1, then sum(n>=1, b(n)*x^n ) = x * prod(n>=1, ((1+x^n)/(1-x^n))^b(n) ); compare to A000081, A004111, and A115593. - Joerg Arndt, Mar 04 2015
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MAPLE
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spec := [S, {B=Set(S), C=PowerSet(S), S=Prod(Z, B, C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=1..20); # Vladeta Jovovic, Feb 10 2005
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MATHEMATICA
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m = 23; A[_] = 0;
Do[A[x_] = Exp[Sum[2 A[x^k] x^k/k, {k, 1, m, 2}]] + O[x]^m // Normal, {m}];
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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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STATUS
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approved
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