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 A053112 Expansion of (-1 + 1/(1-9*x)^9)/(81*x); related to A053108. 5

%I

%S 1,45,1485,40095,938223,19702683,379980315,6839645670,116273976390,

%T 1883638417518,29282015399598,439230230993970,6385731819835410,

%U 90312492880529370,1246312401751305306,16825217423642621631

%N Expansion of (-1 + 1/(1-9*x)^9)/(81*x); related to A053108.

%H G. C. Greubel, <a href="/A053112/b053112.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 G.f.: (-1 + 1/(1-9*x)^9)/(81*x).

%F a(n) = 9^(n-1)*binomial(n+9, 8).

%F a(0)=1, a(1)=45, a(2)=1485, a(3)=40095, a(4)=938223, a(5)=19702683, a(6)=379980315, a(7)=6839645670, a(8)=116273976390, 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). - _Harvey P. Dale_, Apr 27 2013

%t CoefficientList[Series[(-1+1/(1-9*x)^9)/(81*x),{x,0,30}],x] (* or *) LinearRecurrence[{81,-2916,61236,-826686,7440174,-44641044,172186884,-387420489,387420489}, {1,45,1485,40095,938223,19702683, 379980315, 6839645670,116273976390},20] (* _Harvey P. Dale_, Apr 27 2013 *)

%t Table[9^(n - 1)*Binomial[n + 9, 8], {n, 0, 30}] (* _G. C. Greubel_, Aug 16 2018 *)

%o (PARI) vector(30,n,n--; 9^(n-1)*binomial(n+9, 8)) \\ _G. C. Greubel_, Aug 16 2018

%o (MAGMA) [9^(n-1)*Binomial(n+9, 8): n in [0..30]]; // _G. C. Greubel_, Aug 16 2018

%Y Cf. A053108, A053110 - A053113.

%Y Without signs: A078812. With zeros: A049310. Cf. A008310 (T(n, x)), A008312 (U(n, x)).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)