A242172 a(n) = 2^n*binomial((n + 1 + (n mod 2))/2, 1/2).

1, 3, 6, 15, 30, 70, 140, 315, 630, 1386, 2772, 6006, 12012, 25740, 51480, 109395, 218790, 461890, 923780, 1939938, 3879876, 8112468, 16224936, 33801950, 67603900, 140408100, 280816200, 581690700, 1163381400, 2404321560, 4808643120, 9917826435, 19835652870

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Formula

a(2*n) = A002457(n).

a(2*n+1) = A033876(n).

a(2*n+2)/2 = a(2*n+1).

Conjecture: (n+1)*a(n) -2*a(n-1) +4*(-n-1)*a(n-2)=0. - R. J. Mathar, May 11 2014

a(n) = A100071(n+2)/2. - Michel Marcus, Sep 14 2015

Sum_{n>=0} 1/a(n) = 2*Pi/sqrt(3) - 2. - Amiram Eldar, Mar 04 2023

a(n) = (n+2)*binomial(n+1,ceiling(n/2))/2. - Wesley Ivan Hurt, Nov 23 2023

Maple

a := n -> 2^n*binomial((n+1+(n mod 2))/2, 1/2); seq(a(n), n=0..29);

Mathematica

a[n_] := 2^n*Binomial[(n + 1 + Mod[n, 2])/2, 1/2]; Array[a, 33, 0] (* Amiram Eldar, Mar 04 2023 *)

Crossrefs

Cf. A100071, A002457, A033876.

Sequence in context: A357007 A183038 A141023 * A356954 A126982 A256281

Adjacent sequences: A242169 A242170 A242171 * A242173 A242174 A242175

Keyword

nonn

Author

Peter Luschny, May 06 2014

Status

approved