A009133 Expansion of e.g.f. cosh(log(1+x)*cos(x)).

1, 0, 1, -3, 0, 0, 90, -420, 3192, -36792, 344640, -3424080, 40458792, -515760960, 6995451736, -102430659240, 1603858275328, -26656736919808, 469564051796928, -8742335523613056, 171465068564306560, -3533692765499863680

Offset

0,4

Links

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

Formula

a(n) ~ (-1)^n * n! / (2 * Gamma(cos(1)) * n^(1 - cos(1))). - Vaclav Kotesovec, Jul 28 2018

Mathematica

With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]*Cos[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 28 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x)*cos(x)))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x)*Cos(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

Crossrefs

Sequence in context: A215679 A160537 A215516 * A180515 A009138 A175562

Adjacent sequences: A009130 A009131 A009132 * A009134 A009135 A009136

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved