A021784 - OEIS

%I #16 Feb 07 2025 15:46:16

%S 1,21,302,3762,43923,497223,5545264,61398804,677478725,7463074905,

%T 82149266706,903924739926,9944608539607,109397965416267,

%U 1203414334895828,13237742692094328,145616100380861769

%N Expansion of 1/((1-x)(1-4x)(1-5x)(1-11x)).

%H Vincenzo Librandi, <a href="/A021784/b021784.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (21,-139,339,-220).

%F G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-11*x)).

%F a(n) = -1/120 +2^(2n+6)/21 -5^(n+3)/24 +11^(n+3)/420. - _Bruno Berselli_, May 08 2013

%F a(n) = 21*a(n-1) - 139*a(n-2) + 339*a(n-3) - 220*a(n-4). - _Wesley Ivan Hurt_, Jan 01 2024

%t CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 5 x) (1 - 11 x)), {x, 0, 20}], x] (* _Bruno Berselli_, May 08 2013 *)

%t LinearRecurrence[{21,-139,339,-220},{1,21,302,3762},20] (* _Harvey P. Dale_, Feb 07 2025 *)

%o (PARI) Vec(1/((1-x)*(1-4*x)*(1-5*x)*(1-11*x))+O(x^20)) \\ _Bruno Berselli_, May 08 2013

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-5*x)*(1-11*x)))); // _Bruno Berselli_, May 08 2013

%Y Cf. A019040 (first differences).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.