A190818 Expansion of e.g.f.: 1/(1-2*tanh(x)).

1, 2, 8, 44, 320, 2912, 31808, 405344, 5903360, 96722432, 1760811008, 35260703744, 770296217600, 18229999665152, 464622502289408, 12687528814751744, 369557965317079040, 11437129322496131072, 374778854976227115008, 12963259774166774841344, 471986702056014668103680

Offset: 0

Author

Miklos Kristof, May 21 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A011782 (e.g.f. of 1/(1-tanh(x))).

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( 1/(1-2*Tanh(x)) ))); // G. C. Greubel, Dec 03 2023

Maple

E(x):=1/(1-2*tanh(x)):
a[0]:=E(x):
for n from 1 to 30 do a[n]:=diff(a[n-1],x) od:
x:=0:
seq(a[n],n=0..30);

Mathematica

CoefficientList[Series[1/(1-2*Tanh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

PARI

x='x+O('x^66);
Vec(serlaplace(1/(1-2*tanh(x)))) /* Joerg Arndt, May 21 2011 */

SageMath

def A190818_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( 1/(1-2*tanh(x)) ).egf_to_ogf().list()
A190818_list(40) # G. C. Greubel, Dec 03 2023

Formula

E.g.f: 1/(1-2*tanh(x)).

a(n) ~ n! * 2^(n+2)/(3*(log(3))^(n+1)). - Vaclav Kotesovec, Jun 26 2013