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!.

1, 2, 6, 16, 50, 171, 697, 3416, 21126, 169105, 1794683, 25891713, 507686588, 13878639286, 518836271475, 27356839451662, 1968958300103603, 200935638262212462, 27892630019328034846, 5502857784211927305980

Offset: 0

Author

Paul D. Hanna, Jan 01 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A136507, A136508.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m);
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

Mathematica

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 *)

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)}

Sage

def A136509_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    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()
A136509_list(30) # G. C. Greubel, Mar 15 2021