A141413 Inverse binomial transform of A140962.

0, -1, 1, -3, 9, -27, 81, -243, 729, -2187, 6561, -19683, 59049, -177147, 531441, -1594323, 4782969, -14348907, 43046721, -129140163, 387420489, -1162261467, 3486784401, -10460353203, 31381059609, -94143178827, 282429536481, -847288609443

Offset: 0

Author

Paul Curtz, Aug 04 2008

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3).

Crossrefs

Cf. A285066 (alternating row sums, starting here with n >= 2). - Wolfdieter Lang, Apr 23 2017

Cf. A000244, A133494.

Programs

Magma

[0,-1] cat [(-3)^(n-2): n in [2..30]]; // G. C. Greubel, Mar 30 2021

Maple

A141413:= n-> `if`(n<2, -n, (-3)^(n-2)); seq(A141413(n), n=0..30); # G. C. Greubel, Mar 30 2021

Mathematica

CoefficientList[Series[-x(1+2x)/(1+3x), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 24 2013 *)
Join[{0, -1},LinearRecurrence[{-3},{1},26]] (* Ray Chandler, Aug 12 2015 *)

Sage

[-n if n<2 else (-3)^(n-2) for n in (0..30)] # G. C. Greubel, Mar 30 2021

Formula

a(n) = (-1)^n*A133494(n-1), n>0.

G.f.: (-x)*(1 + 2*x)/(1+3*x). - R. J. Mathar, Nov 11 2008

G.f.: x^2/( Q(0)+ 2*x)- x where Q(k) = 1 - x/(x*(k+1) - 1 )/Q(k+1) ; (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 24 2013

E.g.f.: (exp(-3*x) - (1 + 6*x))/9. - Wolfdieter Lang, Apr 19 2017

a(n) = (-3)^(n-2) for n >= 2, with a(0) = 0 and a(1) = -1. - G. C. Greubel, Mar 30 2021

Extensions

Edited and extended by R. J. Mathar, Nov 11 2008