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%I #9 Jul 30 2015 23:35:47
%S 1,2,10,44739260,
%T 28948022309329048855892746252171976963317496166410141009864396001978371888518
%N G.f.: exp( Sum_{n>=1} 2^(n^n) * x^n/n ).
%C Does the g.f. describe an integer sequence?
%C The number of digits in the terms begin: [1, 1, 2, 8, 77, 941, 14045, 247911, ...].
%e G.f.: A(x) = 1 + 2*x + 10*x^2 + 44739260*x^3 +...
%e where
%e log(A(x)) = 2^1*x + 2^4*x^2/2 + 2^27*x^3/3 + 2^256*x^4/4 + 2^3125*x^5/5 + 2^46656*x^6/6 + 2^823543*x^7/7 + 2^16777216*x^8/8 +...+ 2^(n^n)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^m)*x^m/m)+x*O(x^n)), n)}
%o for(n=0,7,print1(a(n),", "))
%Y Cf. A155200, A158110.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 30 2015