A024342 - OEIS

%I #25 Feb 01 2022 07:13:00

%S 2,112,92672,365688832,4411282030592,127206964253949952,

%T 7496936195881447718912,809926025985929119868649472,

%U 148071124873925782667263194693632,43087047288444223765736160658186043392,19011875896715283767147325248912471990730752

%N Expansion of e.g.f. tanh(x)*tan(x), coefficients of powers x^(4*n+2).

%H G. C. Greubel, <a href="/A024342/b024342.txt">Table of n, a(n) for n = 0..120</a>

%F a(n) = 2 * A009837(n).

%t With[{nn=40},Take[CoefficientList[Series[Tanh[x]Tan[x],{x,0,nn}], x] Range[0,nn-2]!,{3,-1,4}]] (* _Harvey P. Dale_, May 02 2012 *)

%o (Magma)

%o m:=50; R<x>:=PowerSeriesRing(Rationals(), m);

%o b:= Coefficients(R!(Laplace( Tan(x)*Tanh(x) )));

%o [b[4*n-3]: n in [1..Floor((m-2)/4)]]; // _G. C. Greubel_, Jan 31 2022

%o (Sage) [factorial(4*n+2)*( tanh(x)*tan(x) ).series(x, 4*n+3).list()[4*n+2] for n in (0..20)] # _G. C. Greubel_, Jan 31 2022

%Y Cf. A000182, A009837, A296628.

%K nonn

%O 0,1

%A _R. H. Hardin_

%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997

%E More terms from _Harvey P. Dale_, May 02 2012