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A363441
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G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ).
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3
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1, 2, 4, 16, 52, 208, 840, 3520, 15008, 65344, 288408, 1288416, 5813744, 26460800, 121333200, 559991712, 2599385536, 12127405952, 56837861376, 267473333120, 1263354463056, 5987210061184, 28461008374480, 135672151034304, 648406644570048
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OFFSET
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0,2
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LINKS
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FORMULA
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A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+2*x^(k+1))^a(k).
a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-2)^(k/d) * a(d-1) ) * a(n-k).
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PROG
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(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^k)*(2*x)^k/k)+x*O(x^n))); Vec(A);
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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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