A159964 a(n) = 2^n*(1-n).

1, 0, -4, -16, -48, -128, -320, -768, -1792, -4096, -9216, -20480, -45056, -98304, -212992, -458752, -983040, -2097152, -4456448, -9437184, -19922944, -41943040, -88080384, -184549376, -385875968, -805306368, -1677721600, -3489660928

Offset: 0

Author

Paul Barry, Apr 28 2009

Keywords

• easy
• sign

Comments

Hankel transform of A124791. Binomial transform of -A060747.

{1} U A159964 is a composition of generating functions of A165747 and A000012, with H=G(F(x)) with F(x) for A000012 and G(x) for A165747. - Oboifeng Dira, Aug 29 2019

Links

• Oboifeng Dira, A Note on Composition and Recursion, Southeast Asian Bulletin of Mathematics (2017), Vol. 41, Issue 6, 849-853.
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Cf. A058922, A060747, A124791.

Programs

Mathematica

LinearRecurrence[{4,-4},{1,0},30] (* Harvey P. Dale, May 02 2016 *)

Formula

G.f.: (1-4x)/(1-2x)^2.

a(n) = -A058922(n). - Jeffrey R. Goodwin, Nov 11 2011

E.g.f.: U(0) where U(k)= 1 - 2*x/(2 - 4/(2 - (k+1)/U(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 18 2012

a(n) = Sum_{k=0..n} (1-2k) * C(n,k). - Wesley Ivan Hurt, Sep 23 2017

From Amiram Eldar, Jan 13 2021: (Start)

Sum_{n>=2} 1/a(n) = -log(2)/2.

Sum_{n>=2} (-1)^n/a(n) = -log(3/2)/2. (End)