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a(n) = Sum_{k=0..2n} (k+1) * A027113(n, 2n-k).
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%I #14 Oct 23 2019 22:07:52

%S 1,7,26,85,264,803,2422,7281,21860,65599,196818,590477,1771456,

%T 5314395,15943214,47829673,143489052,430467191,1291401610,3874204869,

%U 11622614648,34867843987,104603532006,313810596065,941431788244,2824295364783,8472886094402

%N a(n) = Sum_{k=0..2n} (k+1) * A027113(n, 2n-k).

%H Colin Barker, <a href="/A027138/b027138.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,3).

%F For n>1, a(n) = 10*3^(n-2) - n - 1.

%F For n>4, a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3). - _Colin Barker_, Jul 11 2015

%F G.f.: -x*(x^3-2*x^2+2*x+1) / ((x-1)^2*(3*x-1)). - _Colin Barker_, Jul 11 2015

%o (PARI) Vec(-x*(x^3-2*x^2+2*x+1)/((x-1)^2*(3*x-1)) + O(x^50)) \\ _Colin Barker_, Jul 11 2015

%K nonn,easy

%O 1,2

%A _Clark Kimberling_