A136558 G.f.: A(x) = Sum_{n>=0} arcsinh( 2^(2n+1)*x )^(2n+1) / (2n+1)!; a power series in x with integer coefficients.

2, 0, 84, 0, 276892, 0, 111457917800, 0, 6660816097416169260, 0, 66597307693046550483175282456, 0, 120167520447600665027319450022840022638104, 0, 41233407800231936275686869695450406221641586822849599440, 0, 2796405930832642696090353299413183601303402593622351242536692586333202380, 0

Offset: 1

Author

Paul D. Hanna, Jan 10 2008

Keywords

• nonn

Examples

			G.f.: A(x) = 2*x + 84*x^3 + 276892*x^5 + 111457917800*x^7 + ...
		

Links

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

Crossrefs

Cf. A136559.

Programs

Magma

m:=30;
R:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( (&+[Argsinh(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[ArcSinh[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, asinh(2^(2*k+1)*x +x*O(x^n))^(2*k+1)/(2*k+1)!),n)}