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a(n) = Sum_{k=0..2n} (k+1) * A027082(n, 2n-k).
5

%I #19 Sep 08 2022 08:44:49

%S 1,6,20,62,188,566,1700,5102,15308,45926,137780,413342,1240028,

%T 3720086,11160260,33480782,100442348,301327046,903981140,2711943422,

%U 8135830268,24407490806,73222472420,219667417262,659002251788

%N a(n) = Sum_{k=0..2n} (k+1) * A027082(n, 2n-k).

%H Vincenzo Librandi, <a href="/A027107/b027107.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

%F For n>0, a(n) = 7*3^(n-1) - 1.

%F G.f.: (1+2*x-x^2)/(1-4*x+3*x^2). [_Bruno Berselli_, Mar 25 2013]

%F a(n) = 2*A237930(n-1), n>0. - _R. J. Mathar_, Jun 24 2020

%t Join[{1}, Table[7 3^(n-1) - 1, {n, 30}]] (* _Vincenzo Librandi_, Mar 24 2013 *)

%o (Magma) [1] cat [7*3^n-1: n in [0..30]]; // _Vincenzo Librandi_, Mar 24 2013

%K nonn,easy

%O 0,2

%A _Clark Kimberling_