A081279 Binomial transform of Chebyshev coefficients A001794.

1, 8, 47, 238, 1101, 4788, 19899, 79866, 311769, 1189728, 4454919, 16415622, 59659173, 214229772, 761200659, 2679525522, 9353893041, 32409397944, 111534054111, 381480041502, 1297471217661, 4390248981348, 14785128121707

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Formula

a(n) = (2*n^3 + 30*n^2 + 103*n + 81) * 3^(n-4).

a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 81*a(n-4), n>=4.

G.f.: (1-2*x)*(1-x)^2/(1-3*x)^4.

E.g.f.: ((2/3)*x^3 + 4*x^2 + 5*x + 1)*exp(3*x). - Enrique Navarrete, Nov 30 2025

Mathematica

CoefficientList[Series[(1 - 2 x) (1 - x)^2 / (1 - 3 x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{12, -54, 108, -81}, {1, 8, 47, 238}, 30] (* Harvey P. Dale, Jul 27 2015 *)

Prog

(Magma) [(2*n^3+30*n^2 + 103*n + 81)*3^(n - 4): n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

Crossrefs

Cf. A007051, A006234, A081278, A081280.

Sequence in context: A230622 A026983 A296331 * A099110 A106393 A300167

Adjacent sequences: A081276 A081277 A081278 * A081280 A081281 A081282

Keyword

easy,nonn

Author

Paul Barry, Mar 16 2003

Status

approved