A024342 Expansion of e.g.f. tanh(x)*tan(x), coefficients of powers x^(4*n+2).

2, 112, 92672, 365688832, 4411282030592, 127206964253949952, 7496936195881447718912, 809926025985929119868649472, 148071124873925782667263194693632, 43087047288444223765736160658186043392, 19011875896715283767147325248912471990730752

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..120

Crossrefs

Cf. A000182, A009837, A296628.

Programs

Magma

m:=50; R:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Tan(x)*Tanh(x) )));
[b[4*n-3]: n in [1..Floor((m-2)/4)]]; // G. C. Greubel, Jan 31 2022

Mathematica

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 *)

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

Formula

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

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

More terms from Harvey P. Dale, May 02 2012