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

0,3

Comments

Binomial transform of expansion of tan(2x)/2 (0,1,0,8,0,256,...).

Links

Robert Israel, Table of n, a(n) for n = 0..430

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

Maple

seq(I*((4*I)^n*euler(n, -I/4)-1)/2, n=0..30); # Robert Israel, May 26 2016

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 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp(x)*Tan(2*x)/2 ))); // G. C. Greubel, Oct 14 2022
(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

Crossrefs

Cf. A009739.

Sequence in context: A015519 A096977 A353979 * A263547 A152819 A297406

Adjacent sequences: A084095 A084096 A084097 * A084099 A084100 A084101

Keyword

easy,nonn

Author

Paul Barry, May 11 2003

Status

approved