A026543 - OEIS

%I #15 Apr 10 2022 02:22:46

%S 1,27,481,7191,98161,1272663,16005025,197611623,2412718033,

%T 29257382583,353312653057,4255864465671,51186427162417,

%U 615069092006487,7386770412718177,88683539390560935,1064502765417159313

%N Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-12*x)).

%H G. C. Greubel, <a href="/A026543/b026543.txt">Table of n, a(n) for n = 0..915</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (27,-248,900,-1008)

%F a(n) = (-2^n + 225*6^n - 7^(n+3) + 12^(n+2))/25. - _R. J. Mathar_, Jun 23 2013

%F E.g.f.: 1/25 (-exp(2*x) + 225*exp(6*x) - 343*exp(7*x) + 144*exp(12*x)). - _G. C. Greubel_, Apr 09 2022

%t CoefficientList[Series[1/((1-2x)(1-6x)(1-7x)(1-12x)),{x,0,30}],x] (* _Harvey P. Dale_, Apr 18 2019 *)

%o (Magma) [(-2^n +225*6^n -7^(n+3) +12^(n+2))/25: n in [0..30]]; // _G. C. Greubel_, Apr 09 2022

%o (SageMath) [(-2^n +225*6^n -7^(n+3) +12^(n+2))/25 for n in (0..30)] # _G. C. Greubel_, Apr 09 2022

%Y Cf. A000079, A016129, A016304, A026542.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_