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%I A282084 #6 Sep 18 2024 09:44:16
%S A282084 1,4,20,85,255,636,1484,3235,6470,12120,21816,37854,63090,101640,
%T A282084 159720,245322,367983,540540,780780,1110395,1554553,2145572,2925780,
%U A282084 3945045,5260060,6941168,9076912,11769100,15131700,19302480,24449808,30763812,38454765,47771700
%N A282084 Number of n-element subsets of [n+8] having an even sum.
%H A282084 Alois P. Heinz, <a href="/A282084/b282084.txt">Table of n, a(n) for n = 0..1000</a>
%H A282084 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (9, -41, 129, -316, 636, -1084, 1596, -2054, 2326, -2326, 2054, -1596, 1084, -636, 316, -129, 41, -9, 1).
%F A282084 G.f.: -(x^2-x+1)*(x^8-4*x^7+20*x^6-36*x^5+54*x^4-36*x^3+20*x^2-4*x+1) / ((x^2+1)^5*(x-1)^9).
%F A282084 a(n) = A282011(n+8,n).
%e A282084 a(0) = 1: {}.
%e A282084 a(1) = 4: {2}, {4}, {6}, {8}.
%e A282084 a(2) = 20: {1,3}, {1,5}, {1,7}, {1,9}, {2,4}, {2,6}, {2,8}, {2,10}, {3,5}, {3,7}, {3,9}, {4,6}, {4,8}, {4,10}, {5,7}, {5,9}, {6,8}, {6,10}, {7,9}, {8,10}.
%Y A282084 Cf. A282011.
%K A282084 nonn,easy
%O A282084 0,2
%A A282084 _Alois P. Heinz_, Feb 05 2017

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