A136559 G.f.: A(x) = Sum_{n>=0} arctanh( 2^(2n+1)*x )^(2n+1) / (2n+1)!; a power series in x with integer coefficients.

2, 0, 88, 0, 285088, 0, 112173964160, 0, 6667221644498203136, 0, 66605167708510907980664608768, 0, 120169056821375322042225614651624227643392, 0, 41233460218449924405779202537032142206549563511026450432, 0, 2796406262888046560966728498782777223041570797904775508376399120263413760

Offset: 1

Author

Paul D. Hanna, Jan 10 2008

Keywords

• nonn

Comments

2^n divides a(n) for n >= 0.

Examples

			G.f.: A(x) = 2*x + 88*x^3 + 285088*x^5 + 112173964160*x^7 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..49

Crossrefs

Cf. A136558.

Programs

Magma

m:=30;
R:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( (&+[Argtanh(2^(2*j+1)*x)^(2*j+1)/Factorial(2*j+1): j in [0..m+2]]) )); // G. C. Greubel, Mar 15 2021

Mathematica

Rest@With[{m=30}, CoefficientList[Series[Sum[ArcTanh[2^(2*j+1)*x]^(2*j+1)/(2*j + 1)!, {j,0,m+2}], {x,0,m}], x]] (* G. C. Greubel, Mar 15 2021 *)

PARI

{a(n)=polcoeff(sum(k=0,n\2,atanh(2^(2*k+1)*x +x*O(x^n))^(2*k+1)/(2*k+1)!),n)}