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