A009097 Expansion of e.g.f. cos(x)*cos(log(1+x)).

1, 0, -2, 3, -3, 10, -56, 315, -1971, 13788, -105246, 857615, -7266223, 61296222, -465353292, 1982748495, 36246192441, -1600097656520, 43901543199046, -1078930450441413, 25757481055625541, -615789512284527630, 14951870851779274848, -371390034930015683197, 9473760558158414759237

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

a(n) = n! * (LaguerreL(n, -I-n, -I)+LaguerreL(n, -I-n, I)+LaguerreL(n, I-n, -I)+LaguerreL(n, I-n, I))/4. - Mark van Hoeij, Jan 14 2026

Maple

a := n!*(LaguerreL(n, -I-n, -I)+LaguerreL(n, -I-n, I)+LaguerreL(n, I-n, -I)+LaguerreL(n, I-n, I))/4;
simplify([seq(a, n=0..20)]); # Mark van Hoeij, Jan 10 2026

Mathematica

With[{nn=30}, CoefficientList[Series[Cos[x]*Cos[Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 24 2014 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(cos(x)*cos(log(1+x)))) \\ G. C. Greubel, Jul 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)*Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018

Crossrefs

Sequence in context: A152300 A117030 A155758 * A379351 A210194 A210755

Adjacent sequences: A009094 A009095 A009096 * A009098 A009099 A009100

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Jun 24 2014

Status

approved