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A136509 G.f.: A(x) = Sum_{n>=0} (-1)^n * (1 -x -2^n*x^2)^(-1) * log(1 -x -2^n*x^2)^n / n!. 3

%I

%S 1,2,6,16,50,171,697,3416,21126,169105,1794683,25891713,507686588,

%T 13878639286,518836271475,27356839451662,1968958300103603,

%U 200935638262212462,27892630019328034846,5502857784211927305980

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

%H G. C. Greubel, <a href="/A136509/b136509.txt">Table of n, a(n) for n = 0..100</a>

%t With[{m=30}, CoefficientList[Series[Sum[(-1)^j*Log[1-x-2^j*x^2]^j/(j!*(1-x -2^j*x^2)), {j,0,m+2}], {x,0,m}], x]] (* _G. C. Greubel_, Mar 15 2021 *)

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

%o (Magma)

%o m:=30; R<x>:=PowerSeriesRing(Rationals(), m);

%o Coefficients(R!( (&+[(-1)^j*Log(1-x-2^j*x^2)^j/(Factorial(j)*(1 -x -2^j*x^2)) : j in [0..m+2]]) )); // _G. C. Greubel_, Mar 15 2021

%o (Sage)

%o def A136509_list(prec):

%o P.<x> = PowerSeriesRing(QQ, prec)

%o return P( sum((-1)^j*log(1-x -2^j*x^2)^j/(factorial(j)*(1 -x -2^j*x^2)) for j in (0..32)) ).list()

%o A136509_list(30) # _G. C. Greubel_, Mar 15 2021

%Y Cf. A136507, A136508.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 01 2008

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Last modified May 10 14:44 EDT 2021. Contains 343773 sequences. (Running on oeis4.)