A108734 Expansion of (1 + 24*x)^(1/2).

1, 12, -72, 864, -12960, 217728, -3919104, 73903104, -1441110528, 28822210560, -587973095424, 12187078705152, -255928652808192, 5433562167312384, -116433475013836800, 2514963060298874880, -54700446561500528640, 1196974477698717450240, -26333438509371783905280, 582107588101902591590400

Offset: 0

Author

N. J. A. Sloane, Jun 22 2005

Keywords

• sign

Crossrefs

Cf. A108735.

Programs

Mathematica

CoefficientList[Series[(1 + 24 x)^(1/2), {x, 0, 20}], x] (* Vincenzo Librandi, Jan 21 2020 *)

Formula

a(n) = 2^n*A108735(n). - Zak Seidov, Jun 24 2005

D-finite with recurrence: n*a(n) +12*(2*n-3)*a(n-1)=0. - R. J. Mathar, Jan 20 2020

From Amiram Eldar, May 28 2022: (Start)

Sum_{n>=0} 1/a(n) = (672 - 72*arcsinh(1/(2*sqrt(6)))/5)/625.

Sum_{n>=0} 1/a(n) = (480 - 72*arcsin(1/(2*sqrt(6)))/sqrt(23))/529. (End)