OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..381
FORMULA
E.g.f.: -log(1 - x)/2 - log(1 - 3*x)/6. - Andrew Howroyd, Nov 10 2018
3*n*(n+1)*a(n)-4*(n+1)*a(n)+a(n+2)=0. - Robert Israel, Nov 10 2018
MAPLE
ser := series(ln(x+1)/2 + ln(1+3*x)/6, x, 21):
seq((-1)^(n+1)*n!*coeff(ser, x, n), n=0..19);
MATHEMATICA
CoefficientList[Series[Log[x+1]/2 + Log[1+3*x]/6, {x, 0, 50}], x]* Table[(-1)^(n+1)*n!, {n, 0, 50}] (* Stefano Spezia, Nov 10 2018 *)
PROG
(PARI) seq(n)={Vec(serlaplace(-log(1 - x + O(x^n))/2 - log(1 - 3*x + O(x^n))/6), -n)} \\ Andrew Howroyd, Nov 10 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( -Log((1-x)^3*(1-3*x))/6 )); [0] cat [Factorial(n-0)*b[n]: n in [1..(m-1)]]; // G. C. Greubel, Nov 11 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 10 2018
STATUS
approved