A296628 Numerators of coefficients in expansion of e.g.f. tan(x)/tanh(x) (even powers only).

1, 4, 16, 1408, 13568, 606208, 61878272, 1956380672, 21143027712, 348742016303104, 279852224852525056, 5217315235815227392, 118411884225053589504, 842233813811702133686272, 4096134057254358725165056, 3447514330976633343761929207808, 44711197753944482628093599547392

Offset

0,2

Comments

The values of the denominators are similar to A006656 up to n = 138, but differ after.

Links

G. C. Greubel, Table of n, a(n) for n = 0..150

Formula

Numerators of coefficients in expansion of e.g.f. tanh(x)/tan(x) (even powers only, absolute values).

Numerators of coefficients in expansion of e.g.f. sin(x)*cosh(x)/(sinh(x)*cos(x)) (even powers only).

Example

tan(x)/tanh(x) = 1 + (4/3)*x^2/2! + (16/3)*x^4/4! + (1408/21)*x^6/6! + (13568/9)*x^8/8! + ...

Mathematica

nmax = 16; Numerator[Table[(CoefficientList[Series[Tan[x]/Tanh[x], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]]

Prog

(Magma)
m:=50; R<x>:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Tan(x)/Tanh(x) )));
[Numerator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // G. C. Greubel, Jan 31 2022
(Sage) [numerator( factorial(2*n)*( tan(x)/tanh(x) ).series(x, 2*n+3).list()[2*n] ) for n in (0..40)] # G. C. Greubel, Jan 31 2022

Crossrefs

Cf. A000182, A000795, A000965, A006656, A024342.

Sequence in context: A300315 A361196 A355550 * A123234 A198297 A368392

Adjacent sequences: A296625 A296626 A296627 * A296629 A296630 A296631

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Dec 17 2017

Status

approved