A117437 Expansion of e.g.f.: exp(x)*sec(2*x).

1, 1, 5, 13, 105, 441, 5165, 30213, 469585, 3529201, 68525525, 629401213, 14664091065, 159175688361, 4326609913085, 54189700721013, 1683369010256545, 23894940183997921, 835066388382183845, 13248060325188261613

Offset: 0

Author

Paul Barry, Mar 16 2006

Keywords

• easy
• nonn

Comments

Row sums of A117436.

Binomial transform of A002436 (with interpolated zeros).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..425

Crossrefs

Cf. A002436, A117436.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(x)*Sec(2*x) ))); // G. C. Greubel, May 31 2021

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x]Sec[2x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Dec 13 2011 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(x)/cos(2*x))) \\ Michel Marcus, Jun 01 2021

Sage

[factorial(n)*( exp(x)*sec(2*x) ).series(x,n+1).list()[n] for n in (0..30)] # G. C. Greubel, May 31 2021

Formula

a(n) ~ n! * 2^(2*n+1) * (exp(Pi/4) + (-1)^n*exp(-Pi/4)) / Pi^(n+1). - Vaclav Kotesovec, Aug 04 2014