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%I #15 Aug 15 2014 10:23:50
%S 1,1,2,27,540,15273,545424,23441679,1174939901,67222626658,
%T 4321856514871,308474127741229,24206976396414033,2071823443548447053,
%U 192096343794154776046,19183353188372473420096,2052995326868420586298713,234422512754956257129580893
%N G.f. satisfies: A(x) = 1 - x + A(x)^3 - A(x*A(x)^5).
%C 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.
%H Vaclav Kotesovec, <a href="/A242009/b242009.txt">Table of n, a(n) for n = 0..330</a>
%F a(n) ~ c * 5^n * n^(n - 3/5 - 1/5*log(2)) / (exp(n) * (log(2))^n), where c = 0.1494101265204548503053...
%o (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)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A242007 (q=3), A242008 (q=4).
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Aug 11 2014
%E Name corrected by _Vaclav Kotesovec_ and _Paul D. Hanna_, Aug 15 2014
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