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A178852 G.f. satisfies: A(x) = x/(x - B(x^2)) where B(x/A(x)) = x and B(x) is the g.f. of A141200.

%I A178852 #6 Dec 02 2014 08:17:43
%S A178852 1,1,1,2,3,6,10,21,37,79,144,311,580,1262,2393,5236,10055,22095,42857,
%T A178852 94495,184784,408557,804331,1782470,3529190,7836235,15591086,34676360,
%U A178852 69284645,154320310,309480750,690193910,1388679639,3100467566
%N A178852 G.f. satisfies: A(x) = x/(x - B(x^2)) where B(x/A(x)) = x and B(x) is the g.f. of A141200.
%C A178852 The g.f. of A141200 satisfies: B(x) = x + B(B(x)^2).
%H A178852 Paul D. Hanna, <a href="/A178852/b178852.txt">Table of n, a(n) for n = 0..512</a>
%F A178852 a(n) ~ c * d^n / n^(3/2), where d = 2.20085985704067535258..., c = 4.25914484723... if n is even and c = 4.40480643955... if n is odd. - _Vaclav Kotesovec_, Dec 02 2014
%e A178852 G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 10*x^6 + 21*x^7 +...
%e A178852 If B(x) = g.f. of A141200, with B(x/A(x)) = x and B(x) = x + B(B(x)^2), then
%e A178852 B(x) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 72*x^6 + 272*x^7 +... where
%e A178852 x/A(x) = x - (x^2 + x^4 + 2*x^6 + 6*x^8 + 20*x^10 + 72*x^12 + 272*x^14 +...)
%e A178852 A(B(x)) = B(x)/x = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 72*x^5 + 272*x^6 +...
%o A178852 (PARI) {a(n)=local(A=1+x+x^2*O(x^n)); for(i=0,#binary(n)+1, A=x/(x-subst(serreverse(x/A), x, x^2+x^2*O(x^n)))) ; polcoeff(A, n)}
%o A178852 for(n=0,40,print1(a(n),", "))
%Y A178852 Cf. A141200.
%K A178852 nonn
%O A178852 0,4
%A A178852 _Paul D. Hanna_, Aug 11 2010