cp's OEIS Frontend

A027319 a(n) = Sum_{k=0..m} (k+1) * A026082(n, k), where 0 <= k <= m, m=n for n=0,1,2,3; m=2n for n >= 4.

%I A027319 #22 Oct 27 2019 17:30:42
%S A027319 1,3,8,20,120,432,1512,5184,17496,58320,192456,629856,2047032,6613488,
%T A027319 21257640,68024448,216827928,688747536,2181033864,6887475360,
%U A027319 21695547384,68186006064,213856109928,669462604992,2092070640600,6527260398672,20334926626632
%N A027319 a(n) = Sum_{k=0..m} (k+1) * A026082(n, k), where 0 <= k <= m, m=n for n=0,1,2,3; m=2n for n >= 4.
%C A027319 Or, a(n) = Sum_{k=0..m} (k+1)*T(n,m-k), m=n for n=0,1,2,3; m=2n for n >= 4; T given by A026082.
%H A027319 Colin Barker, <a href="/A027319/b027319.txt">Table of n, a(n) for n = 0..1000</a>
%H A027319 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9).
%F A027319 For n>3, a(n) = 8*(n+1)*3^(n-3).
%F A027319 From _Colin Barker_, Feb 17 2016: (Start)
%F A027319 a(n) = 6*a(n-1) - 9*a(n-2) for n>5.
%F A027319 G.f.: (1 - 3*x - x^2 - x^3 + 72*x^4 - 108*x^5) / (1-3*x)^2.
%F A027319 (End)
%t A027319 CoefficientList[Series[(1 - 3 x - x^2 - x^3 + 72 x^4 - 108 x^5)/(1 - 3 x)^2, {x, 0, 26}], x] (* _Michael De Vlieger_, Feb 17 2016 *)
%o A027319 (PARI) Vec((1-3*x-x^2-x^3+72*x^4-108*x^5)/(1-3*x)^2 + O(x^30)) \\ _Colin Barker_, Feb 17 2016
%K A027319 nonn,easy
%O A027319 0,2
%A A027319 _Clark Kimberling_
%E A027319 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 05 2007