A009030 Expansion of e.g.f. cos(log(1+x)*exp(x)).

1, 0, -1, -3, -10, -10, -10, 560, 1220, 24936, -53660, 1220252, -13415576, 140346648, -2192051992, 28246127520, -453007180912, 7224412576832, -124772679402064, 2275818139520912, -43588354415158432, 881182228173945952

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)), n > 0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011

Mathematica

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

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)), 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: A234642 A038228 A213214 * A168331 A212354 A129489

Adjacent sequences: A009027 A009028 A009029 * A009031 A009032 A009033

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved