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%I #2 Mar 30 2012 18:37:22
%S 1,2,10,18,178,338,1450,2562,23234,43906,186602,329298,2276914,
%T 4224530,16898506,29572482,191488770,353405058,1394069578,2434734098,
%U 14073489714,25712245330,97969052778,170225860226,938475356354
%N G.f.: A(x) = exp( Sum_{n>=1} 2^[A001511(n)^2]*x^n/n ) where A001511(n) is the exponent in the highest power of 2 that divides 2n.
%e G.f.: A(x) = 1 + 2*x + 10*x^2 + 18*x^3 + 178*x^4 + 338*x^5 +...
%e log(A(x)) = 2^1*x + 2^4*x^2/2 + 2^1*x^3/3 + 2^9*x^4/4 + 2^1*x^5/5 + 2^4*x^6/6 + 2^1*x^7/7 + 2^16*x^8/8 +...+ 2^[A001511(n)^2]*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,2^(valuation(2*m,2)^2)*x^m/m)+x*O(x^n)),n)}
%Y Cf. A155200, A001511, A000123.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Sep 10 2010
%E Name corrected by _Paul D. Hanna_, Sep 19 2010
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