A009034 Expansion of e.g.f. cos(log(1+x)/exp(x)).

1, 0, -1, 9, -58, 330, -1690, 6580, 5924, -626856, 11483620, -169739812, 2336104168, -31232156280, 411116838184, -5322020904720, 66716820030608, -776290733888320, 7344102656963504, -19147581666874928

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=1..n/2} (-1)^(k)*Sum_{i=2*k..n} binomial(n,i)*(Stirling1(i,2*k)*(2*k)^(n-i)*(-1)^(n-i)), n > 0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011

Mathematica

With[{nn=20}, CoefficientList[Series[Cos[Log[1+x]/Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 14 2014 *)

Prog

(Maxima)
a(n):=if n=0 then 1 else (sum((-1)^(k)*sum(binomial(n, i)*(stirling1(i, 2*k)*(2*k)^(n-i)*(-1)^(n-i)), i, 2*k, n), k, 1, n/2)); /* Vladimir Kruchinin, Jun 29 2011 */
(PARI) x='x+O('x^30); Vec(serlaplace(cos(log(1+x)/exp(x)))) \\ G. C. Greubel, Jul 22 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Log(1+x)/Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 22 2018

Crossrefs

Sequence in context: A099624 A018218 A026750 * A026377 A016209 A196920

Adjacent sequences: A009031 A009032 A009033 * A009035 A009036 A009037

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved