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A309294 (1/2) times the sum of the elements of all subsets of [n] whose sum is divisible by two.

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%I A309294 #10 Aug 27 2021 18:29:54
%S A309294 0,0,1,6,20,60,168,448,1152,2880,7040,16896,39936,93184,215040,491520,
%T A309294 1114112,2506752,5603328,12451840,27525120,60555264,132644864,
%U A309294 289406976,629145600,1363148800,2944401408,6341787648,13623099392,29192355840,62411243520
%N A309294 (1/2) times the sum of the elements of all subsets of [n] whose sum is divisible by two.
%H A309294 Alois P. Heinz, <a href="/A309294/b309294.txt">Table of n, a(n) for n = 0..1000</a>
%H A309294 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A309294 G.f.: -x^2*(4*x^3-4*x^2+1)/(2*x-1)^3.
%t A309294 LinearRecurrence[{6,-12,8},{0,0,1,6,20,60},40] (* _Harvey P. Dale_, Aug 27 2021 *)
%Y A309294 Column k=2 of A309280.
%K A309294 nonn,easy
%O A309294 0,4
%A A309294 _Alois P. Heinz_, Jul 21 2019