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

Author

Ilya Gutkovskiy, Dec 17 2017

Keywords

• nonn
• frac

Comments

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

Examples

			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! + ...
		

Links

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

Crossrefs

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

Programs

Magma

m:=50; R:=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

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}]]

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

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).