cp's OEIS Frontend

A158053 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x*A(x))^n * x^n/n ).

%I A158053 #2 Mar 30 2012 18:37:16
%S A158053 1,1,3,9,37,183,1175,10405,132911,2533697,70988149,2886198771,
%T A158053 168860266189,14046492509383,1668792185650203,280222608364043833,
%U A158053 66930106539423614233,22572046654805538142763
%N A158053 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x*A(x))^n * x^n/n ).
%C A158053 Compare to: M(x) = exp( Sum_{n>=1} (1 + x*M(x))^n * x^n/n ) where M(x) is the g.f. of the Motzkin numbers (A001006).
%e A158053 G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 37*x^4 + 183*x^5 + 1175*x^6 +...
%e A158053 log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 105*x^4/4 + 671*x^5/5 + 5525*x^6/6 +...
%e A158053 log(A(x)) = (1+2x*A(x))*x + (1+4x*A(x))^2*x^2/2 + (1+8x*A(x))^3*x^3/3 +...
%o A158053 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,(1+2^m*x*A)^m*x^m/m+x*O(x^n))));polcoeff(A,n)}
%Y A158053 Cf. A156214.
%K A158053 nonn
%O A158053 0,3
%A A158053 _Paul D. Hanna_, Mar 11 2009