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%I #7 Mar 30 2012 18:37:29
%S 1,1,3,12,56,284,1520,8449,48303,282207,1677489,10112546,61678702,
%T 379919672,2359991520,14767164162,92993252612,588904075546,
%U 3748029131834,23960546501520,153790930664222,990690415079898,6402865318618654,41506375396111624
%N G.f.: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A000069(n), where A000069 lists numbers with an odd number of 1's in their binary expansion.
%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 56*x^4 + 284*x^5 + 1520*x^6 +...
%e where
%e A(x) = 1 + x*A(x) + x^2*A(x)^2 + x^3*A(x)^4 + x^4*A(x)^7 + x^5*A(x)^8 + x^6*A(x)^11 + x^7*A(x)^13 + x^8*A(x)^14 +...
%e and exponents A000069(n) begin:
%e [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,...].
%o (PARI) {A000069(n)=2*n+1-subst(Pol(binary(n)), x, 1)%2}
%o {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^A000069(j))); polcoeff(A, n)}
%Y Cf. A000069 (odious numbers), A195262.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 13 2011
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