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A144139
Chebyshev polynomial of the second kind U(4,n).
9
1, 5, 209, 1189, 3905, 9701, 20305, 37829, 64769, 104005, 158801, 232805, 330049, 454949, 612305, 807301, 1045505, 1332869, 1675729, 2080805, 2555201, 3106405, 3742289, 4471109, 5301505, 6242501, 7303505, 8494309, 9825089, 11306405
OFFSET
0,2
LINKS
FORMULA
G.f.: (1 + 194*x^2 + 184*x^3 + 5*x^4)/(1 - x)^5. - Vincenzo Librandi, May 29 2014
a(n) = 16*n^4-12*n^2+1 = (4*n^2-2*n-1)*(4*n^2+2*n-1). - Vincenzo Librandi, May 29 2014
From Klaus Purath, Sep 08 2022: (Start)
a(n) = A165900(2*n)*A165900(2*n+1).
a(n) = A057722(2*n).
a(n) = 4*(Sum_{i=1..n} A193250(i)) + 1 = 4*A079414(n) + 1.
(End)
MATHEMATICA
lst={}; Do[AppendTo[lst, ChebyshevU[4, n]], {n, 0, 9^2}]; lst
CoefficientList[Series[(1 + 194 x^2 + 184 x^3 + 5 x^4)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2014 *)
PROG
(Magma) [16*n^4-12*n^2+1: n in [0..40]]; // Vincenzo Librandi, May 29 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Changed offset from 1 to 0 by Vincenzo Librandi, May 29 2014
STATUS
approved