A176414 Expansion of (7+8*x)/(1+2*x).

7, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144, 12288, -24576, 49152, -98304, 196608, -393216, 786432, -1572864, 3145728, -6291456, 12582912, -25165824, 50331648, -100663296, 201326592, -402653184, 805306368

Offset: 0

Author

Klaus Brockhaus, Apr 17 2010

Keywords

• sign
• easy

Comments

Inverse binomial transform of A176415.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2).

Crossrefs

Cf. A176415, A110164 (essentially the same), A122803.

Programs

Mathematica

Join[{7},NestList[-2#&,-6,40]] (* Harvey P. Dale, Jun 20 2020 *)

PARI

{for(n=0, 29, print1(polcoeff((7+8*x)/(1+2*x)+x*O(x^n), n), ", "))}

PARI

A176414(n)=3*(-2)^n+!n*4 \\ M. F. Hasler, Apr 19 2015

Formula

a(n) = A110164(n+2) for n > 0.

a(n) = 3*(-2)^n = 3*A122803(n+1) for n > 0; a(0) = 7.

a(n) = -2*a(n-1) for n > 1; a(0) = 7, a(1) = -6.

a(n) = (-1)^n*A132477(n) = (-1)^n*A122391(n+3), n>1.

a(n) = (-1)^n*A111286(n+2) = (-1)^n*A098011(n+4) = (-1)^n*A091629(n) = (-1)^n*A087009(n+3) = (-1)^n*A082505(n+1) = (-1)^n*A042950(n+1) = (-1)^n*A007283(n) = (-1)^n*A003945(n+1), n>0. - R. J. Mathar, Dec 10 2010

E.g.f.: 4 + 3*exp(-2*x). - Alejandro J. Becerra Jr., Feb 15 2021

Extensions

Edited by M. F. Hasler, Apr 19 2015