A009024 Expansion of e.g.f.: x*cos(log(1+x)).

0, 1, 0, -3, 12, -50, 240, -1330, 8400, -59580, 468000, -4018300, 37237200, -367507400, 3802780800, -40373385000, 423927504000, -4048235126000, 25093796832000, 288695417426000, -18721925937000000, 623644389813900000

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:= [0] cat Coefficients(R!(x*Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 22 2018

Mathematica

With[{nmax = 30}, CoefficientList[Series[x*Cos[Log[1 + x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 22 2018 *)

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(x*cos(log(1+x))))) \\ G. C. Greubel, Jul 22 2018

Formula

a(n) = n * A003703(n-1).

a(n+3) = -a(n+2)*(2*n+1)*(n+3)/(n+2) - a(n+1)*(1+n^2)*(n+3)/(n+1), a(0)=0, a(1)=1, a(2)=0. - Sergei N. Gladkovskii, Aug 17 2012

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997