A058581 - OEIS

%I #14 Sep 03 2025 11:41:33

%S 0,1,34,195,644,1605,3366,6279,10760,17289,26410,38731,54924,75725,

%T 101934,134415,174096,221969,279090,346579,425620,517461,623414,

%U 744855,883224,1040025,1216826,1415259,1637020,1883869,2157630,2460191,2793504,3159585,3560514

%N a(n) = (4*n^2 + 2*n - 3)*(2*n - 1)*n/3.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F From _Elmo R. Oliveira_, Sep 03 2025: (Start)

%F G.f.: x*(1 + 29*x + 35*x^2 - x^3)/(1 - x)^5.

%F E.g.f.: x*(3 + 48*x + 48*x^2 + 8*x^3)*exp(x)/3.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

%t Table[(4n^2+2n-3)(2n-1)n/3,{n,0,40}] (* _Harvey P. Dale_, Sep 18 2019 *)

%o (PARI) a(n)=(4*n^2+2*n-3)*(2*n-1)*n/3 \\ _Charles R Greathouse IV_, Oct 21 2022

%o (PARI) concat(0, Vec(-x*(1+29*x+35*x^2-x^3)/(x-1)^5 + O(x^35))) \\ _Elmo R. Oliveira_, Sep 03 2025

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 26 2000

%E More terms from _Elmo R. Oliveira_, Sep 03 2025