A084098 Expansion of e.g.f. exp(x)*tan(2*x)/2.
0, 1, 2, 11, 36, 341, 1702, 23071, 154056, 2691241, 22470602, 479886131, 4808343276, 121361260541, 1418683841902, 41316096677191, 551971861815696, 18218322689532241, 273815850521907602, 10100775754144668251
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..430
Crossrefs
Cf. A009739.
Programs
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Magma
R
:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp(x)*Tan(2*x)/2 ))); // G. C. Greubel, Oct 14 2022 -
Maple
seq(I*((4*I)^n*euler(n,-I/4)-1)/2, n=0..30); # Robert Israel, May 26 2016
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Mathematica
CoefficientList[Series[E^x*Tan[2*x]/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 29 2013 *) Table[I ((4 I)^n*EulerE[n, -I/4] - 1)/2, {n, 0, 20}] (* Benedict W. J. Irwin, May 26 2016 *) -
SageMath
[(i/2)*(-1 + (2*i)^n*sum(binomial(n,j)*(-1-i/2)^j*euler_number(n-j) for j in range(n+1))) for n in range(40)] # G. C. Greubel, Oct 14 2022
Formula
E.g.f.: exp(x)*tan(2*x)/2.
a(n) ~ n! * (exp(Pi/4)-(-1)^n*exp(-Pi/4)) * 4^n/Pi^(n+1). - Vaclav Kotesovec, Sep 29 2013
a(n) = i*((4i)^n*EulerE(n,-i/4)-1)/2. - Benedict W. J. Irwin, May 26 2016
a(n) = (i/2)*( -1 + (2*i)^n * Sum_{j=0..n} binomial(n,j)*(-1 - i/2)^j*EulerE(n-j) ). - G. C. Greubel, Oct 14 2022
Comments