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A363442
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G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (3*x)^k/k ).
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3
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1, 3, 9, 54, 270, 1620, 9828, 61884, 397062, 2597508, 17232831, 115722918, 784996434, 5371325217, 37029240315, 256948639344, 1793271890988, 12579466538187, 88645665923244, 627235978623318, 4454619888380355, 31743030458459169, 226890102674671245
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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+3*x^(k+1))^a(k).
a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-3)^(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)*(3*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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