A143126 a(n) = (1-2n)*2^n.

1, -2, -12, -40, -112, -288, -704, -1664, -3840, -8704, -19456, -43008, -94208, -204800, -442368, -950272, -2031616, -4325376, -9175040, -19398656, -40894464, -85983232, -180355072, -377487360, -788529152, -1644167168, -3422552064, -7113539584, -14763950080

Offset

0,2

Comments

Hankel transform of abs(A002420) (which is 2*0^n - binomial(2n,n)/(2n-1)).

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (4,-4).

Formula

G.f.: (1-6x)/(1-2x)^2;

a(n) = Sum_{k=0..n} A121314(n,k)*(-1)^k*2^(3n-2k). - Philippe Deléham, Oct 31 2008

From Amiram Eldar, Oct 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 1 - arcsinh(1)/sqrt(2).

Sum_{n>=0} (-1)^n/a(n) = 1 + arctan(1/sqrt(2))/sqrt(2). (End)

Mathematica

a[n_] := (1-2n)*2^n; Array[a, 40, 0] (* Amiram Eldar, Oct 01 2022 *)

Crossrefs

Cf. A002420, A118417, A121314.

Sequence in context: A290131 A008911 A005719 * A118417 A069144 A013194

Adjacent sequences: A143123 A143124 A143125 * A143127 A143128 A143129

Keyword

easy,sign

Author

Paul Barry, Jul 26 2008

Status

approved