A321398 a(n) = (-1)^(n+1)*n!* [x^n](log(x + 1)/2 + log(3*x + 1)/6).

0, 1, 2, 10, 84, 984, 14640, 262800, 5513760, 132289920, 3571464960, 107140320000, 3535590643200, 127280784153600, 4963944354969600, 208485575730432000, 9381849600195072000, 450328759886573568000, 22966766398527823872000, 1240205379118128783360000

Offset: 0

Author

Peter Luschny, Nov 10 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..381

Crossrefs

Cf. A133942 (n=1), A000165 (n=2), this sequence (n=3), A320962 (limit).

Programs

Magma

m:=30; R:=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

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 *)

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

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