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A242009
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G.f. satisfies: A(x) = 1 - x + A(x)^3 - A(x*A(x)^5).
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3
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1, 1, 2, 27, 540, 15273, 545424, 23441679, 1174939901, 67222626658, 4321856514871, 308474127741229, 24206976396414033, 2071823443548447053, 192096343794154776046, 19183353188372473420096, 2052995326868420586298713, 234422512754956257129580893
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OFFSET
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0,3
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COMMENTS
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In general, if g.f. satisfies: A(x) = 1 - x + A(x)^3 - A(x*A(x)^q), q>=3, then a(n) ~ c(q) * q^n * n^(n - 3/q + (1/2-7/(2*q))*log(2)) / (exp(n) * (log(2))^n), where c(q) is a constant independent on n.
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LINKS
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FORMULA
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a(n) ~ c * 5^n * n^(n - 3/5 - 1/5*log(2)) / (exp(n) * (log(2))^n), where c = 0.1494101265204548503053...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 2*A - (1-x + A^3 - subst(A, x, x*A^5 +x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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