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%I #23 Jul 20 2023 16:30:41
%S 0,1,14,171,2044,24341,289674,3446911,41014904,488035881,5807129734,
%T 69098919251,822206626164,9783419785021,116412711336194,
%U 1385192464081191,16482376713731824,196123462390215761
%N a(n) = 5^(n-1) * U(n-1, 7/5) where U is the Chebyshev polynomial of the second kind.
%H G. C. Greubel, <a href="/A099158/b099158.txt">Table of n, a(n) for n = 0..925</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-25).
%F G.f.: x/(1 - 14*x + 25*x^2).
%F E.g.f.: exp(7*x)*sinh(2*sqrt(6)*x)/sqrt(6).
%F a(n) = 14*a(n-1) - 25*a(n-2).
%F a(n) = sqrt(6)*(sqrt(6)+1)^(2*n)/24 - sqrt(6)*(sqrt(6)-1)^(2*n)/24.
%F a(n) = Sum_{k=0..n} binomial(2n, 2k+1)*6^k/2.
%F a(n) = 5^(n-1)*U(n-1, 7/5), where U is the Chebyshev polynomial of the second kind.
%t LinearRecurrence[{14,-25}, {0,1}, 40] (* _G. C. Greubel_, Jul 20 2023 *)
%o (PARI) a(n) = 5^(n-1)*polchebyshev(n-1, 2, 7/5); \\ _Michel Marcus_, Sep 08 2019
%o (Magma) [n le 2 select n-1 else 14*Self(n-1) -25*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jul 20 2023
%o (SageMath)
%o A099158=BinaryRecurrenceSequence(14,-25,0,1)
%o [A099158(n) for n in range(41)] # _G. C. Greubel_, Jul 20 2023
%Y Cf. A099141, A099157.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 01 2004
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