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A179488 G.f.: A(x) satisfies A(x) = x/(1 - (1-2x)*A( x/(1-2x) )).

%I A179488 #21 Jun 05 2021 01:52:17
%S A179488 1,1,2,7,32,172,1052,7177,53792,437992,3841772,36060262,360234512,
%T A179488 3812425912,42576007352,500022862357,6157034292032,79278216024592,
%U A179488 1064888929532492,14890014669234922,216315676347260912
%N A179488 G.f.: A(x) satisfies A(x) = x/(1 - (1-2x)*A( x/(1-2x) )).
%F A179488 G.f.: x/(1 - (1-2*x)*x/(1-2*x - (1-4*x)*x/(1-4*x - (1-6*x)*x/(1-6*x - (1-8*x)*x/(1-8*x - ... (continued fraction).
%F A179488 From _Gary W. Adamson_, Jul 21 2011: (Start)
%F A179488 a(n) = upper left term of M^(n-1), M = an infinite square production matrix as follows (with the odd integers as the main diagonal):
%F A179488   1, 1, 0, 0, 0, ...
%F A179488   1, 3, 1, 0, 0, ...
%F A179488   1, 1, 5, 1, 0, ...
%F A179488   1, 1, 1, 7, 1, ...
%F A179488   1, 1, 1, 1, 9, ...
%F A179488   ... (End)
%F A179488 G.f.: 2/E(0) where E(k) = 1 + 1/(1 + 2*x/(1 - 2*(2*k+3)*x/E(k+1))); (continued fraction, 3-step). - _Sergei N. Gladkovskii_, Sep 20 2012
%F A179488 G.f.: 1/Q(0) where Q(k) = 1 - x*(2*k+1)/( 1 - x/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Mar 22 2013
%F A179488 G.f.: 1/x - Q(0)/x, where Q(k) = 1 - x/(1 - (2*k+1)*x/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Sep 27 2013
%e A179488 G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 32*x^5 + 172*x^6 + ...
%e A179488 A(x) = x + x*A(x) + x*A(x)*A(x/(1-2x)) + x*A(x)*A(x/(1-2x))*A(x/(1-4x)) + x*A(x)*A(x/(1-2x))*A(x/(1-4x))*A(x/(1-6x)) + ...
%o A179488 (PARI) {a(n)=local(A=x+x^2);for(i=1,n,A=x/(1-(1-2*x)*subst(A,x,x/(1-2*x+x^2*O(x^n)))));polcoeff(A,n)}
%Y A179488 Cf. variants: A074664, A179489.
%K A179488 nonn
%O A179488 1,3
%A A179488 _Paul D. Hanna_, Aug 13 2010