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G.f.: A(x) = Sum_{n>=0} log(1 + x/(1-2^n*x))^n/n!.
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%I #2 Mar 30 2012 18:37:17

%S 1,1,2,6,26,152,1202,12840,184060,3552960,92338448,3237738008,

%T 153574021372,9872941474544,862850471831896,102720981260693424,

%U 16701084112350547436,3715705202756433837504,1133547354784950481434016

%N G.f.: A(x) = Sum_{n>=0} log(1 + x/(1-2^n*x))^n/n!.

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 26*x^4 + 152*x^5 +...

%e A(x) = Sum_{n>=0} log(1 + x + 2^n*x^2 + 4^n*x^3 + 8^n*x^4 +..)^n/n!.

%e A(x) = 1 + log(1+x/(1-2x)) + log(1+x/(1-4x))^2/2! + log(1+x/(1-8x))^3/3! +...

%o (PARI) {a(n)=polcoeff(sum(m=0,n,log(1+x/(1-2^m*x+x*O(x^n)))^m/m!),n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 08 2009