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

1, 1, 3, 7, 23, 81, 361, 1923, 13113, 114433, 1315783, 20286135, 420198791, 12003852369, 464295025509, 25153926114307, 1847231277588405, 191568316434991857, 26902669460380225411, 5357197471644242149975

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, A136509.

Programs

Magma

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

Mathematica

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 *)

PARI

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

Sage

def A136508_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( sum((-1)^j*log(1-x -2^j*x^2)^j/factorial(j) for j in (0..32)) ).list()
A136508_list(30) # G. C. Greubel, Mar 15 2021