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Expansion of 1/((1-6*x)*(1-10*x)).
1

%I #25 Nov 13 2024 17:01:40

%S 1,16,196,2176,23056,238336,2430016,24580096,247480576,2484883456,

%T 24909300736,249455804416,2496734826496,24980408958976,

%U 249882453753856,2499294722523136,24995768335138816,249974610010832896,2499847660064997376,24999085960389984256,249994515762339905536,2499967094574039433216

%N Expansion of 1/((1-6*x)*(1-10*x)).

%H G. C. Greubel, <a href="/A016173/b016173.txt">Table of n, a(n) for n = 0..990</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-60).

%F a(n) = (10^(n+1) - 6^(n+1))/4. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008

%F a(n) = 16*a(n-1) - 60*a(n-2). - _Philippe Deléham_, Jan 01 2009

%F a(n) = 10*a(n-1) + 6^n, a(0)=1. - _Vincenzo Librandi_, Feb 09 2011

%F E.g.f.: (1/2)*(5*exp(10*x) - 3*exp(6*x)). - _G. C. Greubel_, Nov 13 2024

%t Table[(10^(n+1) - 6^(n+1))/4, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011 *)

%t CoefficientList[Series[1/((1-6x)(1-10x)), {x,0,40}], x] (* _Harvey P. Dale_, Mar 12 2011 *)

%o (Magma) [(10^(n+1) - 6^(n+1))/4: n in [0..40]]; // _G. C. Greubel_, Nov 13 2024

%o (Python)

%o def A016173(n): return (pow(10,n+1) - pow(6,n+1))//4

%o print([A016173(n) for n in range(41)]) # _G. C. Greubel_, Nov 13 2024

%Y Cf. A016129.

%K nonn,changed

%O 0,2

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Nov 13 2024