A239739 a(n) = n*4^(2*n+1).

0, 64, 2048, 49152, 1048576, 20971520, 402653184, 7516192768, 137438953472, 2473901162496, 43980465111040, 774056185954304, 13510798882111488, 234187180623265792, 4035225266123964416, 69175290276410818560, 1180591620717411303424, 20070057552195992158208

Offset

0,2

Comments

Appears in asymptotic expansions of the logarithm of the central binomial and the Catalan numbers. (See Kessler and Schiff, page 2.)

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

D. Kessler and J. Schiff, The asymptotics of factorials, binomial coefficients and Catalan numbers. April 2006.

Index entries for linear recurrences with constant coefficients, signature (32,-256).

Formula

G.f.: 64*x / (1 - 16*x)^2. [Bruno Berselli, Mar 26 2014]

(n-1)*a(n) - 16*n*a(n-1) = 0. [Bruno Berselli, Mar 26 2014]

a(n) = n*A013709(n). - Michel Marcus, Jan 30 2016

a(n) = 16*A193132(n)/3. - R. J. Mathar, May 18 2026

Mathematica

CoefficientList[Series[64 x /(1 - 16 x)^2, {x, 0, 20}], x] (* Vincenzo Librandi, Apr 25 2014 *)
LinearRecurrence[{32, -256}, {0, 64}, 20] (* Harvey P. Dale, May 06 2021 *)

Prog

(Magma) [n*4^(2*n+1): n in [0..25]]; // Vincenzo Librandi, Apr 25 2014

Crossrefs

Cf. A219931, A220002, A220422, A267796, A013709.

Sequence in context: A324492 A035727 A035801 * A017727 A089458 A283280

Adjacent sequences: A239736 A239737 A239738 * A239740 A239741 A239742

Keyword

nonn,easy

Author

Peter Luschny, Mar 26 2014

Status

approved