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A321398 a(n) = (-1)^(n+1)*n!* [x^n](log(x + 1)/2 + log(3*x + 1)/6). 2
0, 1, 2, 10, 84, 984, 14640, 262800, 5513760, 132289920, 3571464960, 107140320000, 3535590643200, 127280784153600, 4963944354969600, 208485575730432000, 9381849600195072000, 450328759886573568000, 22966766398527823872000, 1240205379118128783360000 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A250117 A244627 A113332 * A180715 A107863 A065866

Adjacent sequences:  A321395 A321396 A321397 * A321399 A321400 A321401

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 10 2018

STATUS

approved

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Last modified May 19 07:24 EDT 2019. Contains 323386 sequences. (Running on oeis4.)