

A020542


a(n) = 5th Chebyshev polynomial (second kind) evaluated at 2^n.


1



6, 780, 30744, 1032240, 33423456, 1072693440, 34351350144, 1099444519680, 35183835219456, 1125895611878400, 36028762659231744, 1152921229728952320, 36893485948395872256, 1180591603125225308160, 37778931722219673452544, 1208925818488729268060160
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


LINKS

Colin Barker, Table of n, a(n) for n = 0..663
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (42,336,512).


FORMULA

From Colin Barker, May 03 2015: (Start)
a(n) = 2^(1+n)*(34^(2+n)+16^(1+n))
a(n) = 42*a(n1)336*a(n2)+512*a(n3) for n>2.
G.f.: 6*(88*x+1) / ((2*x1)*(8*x1)*(32*x1)).
(End)


MAPLE

with(orthopoly):seq(U(5, 2^i), i=0..24);


MATHEMATICA

Table[ChebyshevU[5, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
LinearRecurrence[{42, 336, 512}, {6, 780, 30744}, 16] (* JeanFrançois Alcover, Dec 04 2017 *)


PROG

(PARI) Vec(6*(88*x+1)/((2*x1)*(8*x1)*(32*x1)) + O(x^100)) \\ Colin Barker, May 03 2015
(PARI) a(n) = polchebyshev(5, 2, 2^n) \\ Michel Marcus, May 03 2015


CROSSREFS

Sequence in context: A214009 A088217 A242850 * A045480 A006114 A321426
Adjacent sequences: A020539 A020540 A020541 * A020543 A020544 A020545


KEYWORD

nonn,easy


AUTHOR

Simon Plouffe


STATUS

approved



