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%I #28 Oct 01 2023 12:30:31
%S 1,81,3645,120285,3247695,75996063,1595917323,30778405515,
%T 554011299270,9418192087590,152574711818958,2371843247367438,
%U 35577648710511570,517244277406668210,7315311923322878970
%N Expansion of 1/(1 - 9*x)^9.
%H Vincenzo Librandi, <a href="/A053108/b053108.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (81, -2916, 61236, -826686, 7440174, -44641044, 172186884, -387420489, 387420489).
%F a(n) = 9^n*binomial(n+8, 8).
%F G.f.: 1/(1 - 9*x)^9.
%F a(n) = 81*a(n-1) - 2916*a(n-2) + 61236*a(n-3) - 826686*a(n-4) + 7440174*a(n-5) - 44641044*a(n-6) + 172186884*a(n-7) - 387420489*a(n-8) + 387420489*a(n-9); a(0)=1, a(1)=81, a(2)=3645, a(3)=120285, a(4)=3247695, a(5)=75996063, a(6)=1595917323, a(7)=30778405515, a(8)=554011299270. - _Harvey P. Dale_, Jan 21 2012
%t CoefficientList[Series[1/(1-9x)^9,{x,0,30}],x] (* _Harvey P. Dale_, Jan 21 2012 *)
%o (Sage)[lucas_number2(n, 9, 0)*binomial(n,8)/9^8 for n in range(8, 23)] # _Zerinvary Lajos_, Mar 13 2009
%o (Magma) [Binomial(n+8, 8)*9^n: n in [0..20]]; // _Vincenzo Librandi_, Oct 13 2011
%o (PARI) vector(20, n, n--; 9^n*binomial(n+8,8)) \\ _G. C. Greubel_, Aug 15 2018
%Y Cf. A053107.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_
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