A009125 Expansion of e.g.f. cosh(log(1+tan(x))).

1, 0, 1, -3, 20, -120, 976, -8568, 88640, -1011840, 12933376, -180964608, 2767631360, -45799004160, 816582578176, -15594628021248, 317710534983680, -6876762625966080, 157606194409701376, -3812723805066559488

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

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

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Tan(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

Mathematica

CoefficientList[Series[(1 + (1 + Tan[x])^2)/(2*(1 + Tan[x])), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

PARI

x='x+O('x^30); Vec(serlaplace(cosh(log(1+tan(x))))) \\ G. C. Greubel, Jul 28 2018

Formula

E.g.f.: cosh(log(1+tan(x))).

a(n) ~ n! * (-1)^n * 4^n / Pi^(n+1). - Vaclav Kotesovec, Jan 22 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997