A243130 1024*n^10 - 2304*n^8 + 1792*n^6 - 560*n^4 + 60*n^2 - 1.

-1, 11, 564719, 46611179, 929944511, 9127651499, 58130412911, 276182038859, 1061324394239, 3472236254411, 10011386405999, 26069206375211, 62418042417599, 139296285729899, 292810020137711, 584605483663499, 1116034330278911, 2048348816684939, 3630829342034159

Offset

0,2

Comments

Chebyshev polynomial of the second kind U(10,n).

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: (-1 + 22*x + 564543*x^2 + 40400040*x^3 + 448278942*x^4 + 1368702180*x^5 + 1368701718*x^6 + 448279272*x^7 + 40399875*x^8 + 564598*x^9 + 11*x^10)/(1 - x)^11.

a(n) = (32*n^5 - 16*n^4 - 32*n^3 +12*n^2 + 6*n - 1)*(32*n^5 + 16*n^4 - 32*n^3 -12*n^2 + 6*n + 1).

Mathematica

Table[ChebyshevU[10, n], {n, 0, 20}] (* or *) Table[1024 n^10 - 2304 n^8 + 1792 n^6 - 560 n^4 + 60 n^2 - 1, {n, 0, 20}]
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {-1, 11, 564719, 46611179, 929944511, 9127651499, 58130412911, 276182038859, 1061324394239, 3472236254411, 10011386405999}, 20] (* Harvey P. Dale, Dec 10 2023 *)

Prog

(Magma) [1024*n^10-2304*n^8+1792*n^6-560*n^4+60*n^2-1: n in [0..20]];

Crossrefs

Cf. A144138, A144139, A242850, A242851.

Sequence in context: A090102 A320625 A219013 * A253632 A112854 A211238

Adjacent sequences: A243127 A243128 A243129 * A243131 A243132 A243133

Keyword

sign,easy

Author

Vincenzo Librandi, May 30 2014

Status

approved