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A136508 G.f.: A(x) = Sum_{n>=0} (-1)^n * log(1 - x - 2^n*x^2)^n / n! .

%I A136508 #6 Mar 15 2021 01:55:25
%S A136508 1,1,3,7,23,81,361,1923,13113,114433,1315783,20286135,420198791,
%T A136508 12003852369,464295025509,25153926114307,1847231277588405,
%U A136508 191568316434991857,26902669460380225411,5357197471644242149975
%N A136508 G.f.: A(x) = Sum_{n>=0} (-1)^n * log(1 - x - 2^n*x^2)^n / n! .
%H A136508 G. C. Greubel, <a href="/A136508/b136508.txt">Table of n, a(n) for n = 0..100</a>
%t A136508 With[{m = 30}, CoefficientList[Series[Sum[(-1)^j*Log[1 -x -2^j*x^2]^j/j!, {j, 0, m+2}], {x, 0, m}], x]] (* _G. C. Greubel_, Mar 15 2021 *)
%o A136508 (PARI) {a(n)=polcoeff(sum(i=0,n,(-1)^i*log(1-x-2^i*x^2 +x*O(x^n))^i/i!),n)}
%o A136508 (Magma)
%o A136508 m:=30; R<x>:=PowerSeriesRing(Rationals(), m);
%o A136508 Coefficients(R!( (&+[(-1)^j*Log(1-x-2^j*x^2)^j/Factorial(j) : j in [0..m+2]]) )); // _G. C. Greubel_, Mar 15 2021
%o A136508 (Sage)
%o A136508 def A136508_list(prec):
%o A136508     P.<x> = PowerSeriesRing(QQ, prec)
%o A136508     return P( sum((-1)^j*log(1-x -2^j*x^2)^j/factorial(j) for j in (0..32)) ).list()
%o A136508 A136508_list(30) # _G. C. Greubel_, Mar 15 2021
%Y A136508 Cf. A136507, A136509.
%K A136508 nonn
%O A136508 0,3
%A A136508 _Paul D. Hanna_, Jan 01 2008