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Expansion of e.g.f. exp( x - Sum_{k>=1} x^(2^k)/2^k ).
1

%I #17 Jul 07 2024 13:51:54

%S 1,1,0,-2,-8,-24,16,400,-3072,-38528,-18944,1287936,17843200,

%T 149045248,-188786688,-12007184384,-1265929355264,-20275964313600,

%U 3871935889408,2355175169523712,45658709327609856,565591105847689216,-1448855443865600000

%N Expansion of e.g.f. exp( x - Sum_{k>=1} x^(2^k)/2^k ).

%H Seiichi Manyama, <a href="/A374364/b374364.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: Product_{k>=1} (1 + x^(2*k-1))^(mu(2*k-1)/(2*k-1)), where mu() is the Moebius function.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-sum(k=1, ceil(log(N+1)/log(2)), x^2^k/2^k))))

%Y Cf. A005388, A008683, A117209, A293604.

%K sign

%O 0,4

%A _Seiichi Manyama_, Jul 06 2024