A168150 Inverse binomial transform of A026741.

0, 1, -1, 3, -8, 20, -48, 112, -256, 576, -1280, 2816, -6144, 13312, -28672, 61440, -131072, 278528, -589824, 1245184, -2621440, 5505024, -11534336, 24117248, -50331648, 104857600, -218103808, 452984832, -939524096, 1946157056, -4026531840, 8321499136, -17179869184

Offset: 0

Author

Paul Curtz, Nov 19 2009

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-4,-4).

Crossrefs

Cf. A001792, A026741, A108189.

Programs

Magma

[0,1] cat [(-2)^(n-3)*n: n in [2..35]]; // Vincenzo Librandi, Jul 15 2016

Mathematica

Join[{0, 1, -1, 3}, LinearRecurrence[{-4, -4}, {-8, 20}, 50]] (* G. C. Greubel, Jul 14 2016 *)
CoefficientList[Series[x (1 + 3 x + 3 x^2) / (1 + 2 x)^2, {x, 0, 33}], x] (* Vincenzo Librandi, Jul 15 2016 *)

PARI

a(n)=(-2)^if(n>1,n-3)*n  \\ M. F. Hasler, Jan 25 2012

Formula

a(n+2) = (-1)^(n+1) * A001792(n).

From R. J. Mathar, Nov 23 2009: (Start)

a(n) = -4*a(n-1) -4*a(n-2) = (-2)^(n-3)*n, n>3.

G.f.: x*(1 + 3*x + 3*x^2)/(1 + 2*x)^2. (End)

Extensions

Comments turned into formulas, out-of-scope material moved to A026741 by R. J. Mathar, Nov 23 2009