A081628 a(n) = 2*(-1)^n - (-5)^n.

1, 3, -23, 123, -623, 3123, -15623, 78123, -390623, 1953123, -9765623, 48828123, -244140623, 1220703123, -6103515623, 30517578123, -152587890623, 762939453123, -3814697265623, 19073486328123, -95367431640623, 476837158203123, -2384185791015623, 11920928955078123

Offset: 0

Author

Paul Barry, Mar 26 2003

Keywords

• easy
• sign

Comments

Inverse binomial transform of A081629.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-6,-5).

Crossrefs

Cf. A000351, A033999, A081629.

Programs

Magma

[2*(-1)^n-(-5)^n: n in [0..25]]; // Vincenzo Librandi, Aug 09 2013

Mathematica

CoefficientList[Series[(1 + 9 x) / ((1 + x) (1 + 5 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)
LinearRecurrence[{-6,-5},{1,3},30] (* Harvey P. Dale, Jan 08 2021 *)

Formula

G.f.: (1+9*x)/((1+x)*(1+5*x)).

E.g.f.: 2*exp(-x) - exp(-5*x).

a(n) = A033999(n)*(2 - A000351(n)). - Elmo R. Oliveira, Dec 05 2023