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

Author

Paul Barry, Mar 16 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A007051, A006234, A081278, A081280.

Programs

Magma

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

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 *)

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) +8*1a(n-4), a(0)=1, a(1)=8, a(2)=47, a(3)=238.

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