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A099158 a(n) = 5^(n-1) * U(n-1, 7/5) where U is the Chebyshev polynomial of the second kind. 0
0, 1, 14, 171, 2044, 24341, 289674, 3446911, 41014904, 488035881, 5807129734, 69098919251, 822206626164, 9783419785021, 116412711336194, 1385192464081191, 16482376713731824, 196123462390215761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (14,-25).

FORMULA

G.f.: x/(1 - 14*x + 25*x^2).

E.g.f.: exp(7*x)*sinh(2*sqrt(6)*x)/sqrt(6).

a(n) = 14*a(n-1) - 25*a(n-2).

a(n) = sqrt(6)*(sqrt(6)+1)^(2*n)/24 - sqrt(6)*(sqrt(6)-1)^(2*n)/24.

a(n) = Sum_{k=0..n} binomial(2n, 2k+1)*6^k/2.

a(n) = 5^(n-1)*U(n-1, 7/5), where U is the Chebyshev polynomial of the second kind.

PROG

(PARI) a(n) = 5^(n-1)*polchebyshev(n-1, 2, 7/5); \\ Michel Marcus, Sep 08 2019

CROSSREFS

Cf. A099141.

Sequence in context: A199529 A098299 A254811 * A014882 A048443 A191690

Adjacent sequences:  A099155 A099156 A099157 * A099159 A099160 A099161

KEYWORD

easy,nonn,changed

AUTHOR

Paul Barry, Oct 01 2004

STATUS

approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)