A009130 Expansion of e.g.f. cosh(log(1+x))/cos(x).

1, 0, 2, -3, 23, -90, 676, -4305, 37533, -325332, 3366166, -36472095, 443702291, -5732993838, 80707226328, -1207617980205, 19365202513145, -328878787017000, 5925189947339626, -112532916285619515, 2251485624038961615

Offset

0,3

Links

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

Formula

a(n) ~ n! * (-1)^n * sin(1) / sin(2). - Vaclav Kotesovec, Jan 22 2015

Mathematica

CoefficientList[Series[((1 + (1 + x)^2)*Sec[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)
With[{nn=20}, CoefficientList[Series[Cosh[Log[1+x]]/Cos[x], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 21 2021 *)

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: A350523 A262730 A260127 * A093504 A370279 A009180

Adjacent sequences: A009127 A009128 A009129 * A009131 A009132 A009133

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved