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A171184 G.f. satisfies: A(x) = A(x)^2 - x*A(2x). 1

%I

%S 1,1,1,2,11,150,4474,277044,34897875,8863484966,4520306307806,

%T 4619735172579132,9451969086159465470,38696352180977336223228,

%U 316923105439684775855164884,5191834235882300670847354499880

%N G.f. satisfies: A(x) = A(x)^2 - x*A(2x).

%H Vaclav Kotesovec, <a href="/A171184/b171184.txt">Table of n, a(n) for n = 0..80</a>

%F a(n) = 2^(n-1)*a(n-1) - Sum_{k=1..n-1} a(k)*a(n-k) for n>0 with a(0)=1.

%F G.f.: A(x) = 1 + x*A(2x)/A(x).

%F a(n) ~ c * 2^(n*(n-1)/2), where c = 0.1279729718630988916686793555289366866035815816364398379... . - _Vaclav Kotesovec_, Aug 08 2014

%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 11*x^4 + 150*x^5 + 4474*x^6 +...

%e A(x)^2 = 1 + 2*x + 3*x^2 + 6*x^3 + 27*x^4 + 326*x^5 + 9274*x^6 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+x*subst(A,x,2*x +x*O(x^n))/(A+x*O(x^n)));polcoeff(A,n)}

%o (PARI) {a(n)=if(n==0,1,2^(n-1)*a(n-1)-sum(k=1,n-1,a(k)*a(n-k)))}

%K nonn

%O 0,4

%A _Paul D. Hanna_, Dec 09 2009

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)