A009007 Expansion of 1/cos(log(1+x)).

1, 0, 1, -3, 16, -100, 760, -6720, 67940, -772560, 9760100, -135617900, 2055532400, -33748556400, 596675513200, -11302050942000, 228340292986000, -4901379615184000, 111394219174810000, -2672242230261006000

Offset: 0

Author

R. H. Hardin, Simon Plouffe

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 21 2018

Maple

seq(coeff(series(factorial(n)*(1/cos(log(1+x))), x,n+1),x,n),n=0..20); # Muniru A Asiru, Jul 21 2018

Mathematica

With[{nn = 50}, CoefficientList[Series[1/Cos[Log[1 + x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Apr 11 2014 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/cos(log(1+x)))) \\ G. C. Greubel, Jul 21 2018

Formula

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