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%I #11 Jun 10 2018 17:39:51
%S 0,5,25,110,350,1001,2485,5720,12120,24310,46126,83980,146860,248710,
%T 408430,653752,1021240,1562275,2343055,3453450,5007002,7153575,
%U 10079355,14024400,19282640,26225628,35302540,47071640,62200280,81505820,105955628,136719440
%N Number of 9-element subsets of [n+9] having an even sum.
%H Alois P. Heinz, <a href="/A282077/b282077.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-15,35,1,-65,45,45,-65,1,35,-15,-5,5,-1).
%F G.f.: x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^10).
%F a(n) = ((384 + 400*n + 140*n^2 + 20*n^3 + n^4)*(-945*(-1+(-1)^n) + 3378*n + 1900*n^2 + 460*n^3 + 50*n^4 + 2*n^5)) / 1451520. - _Colin Barker_, Feb 06 2017
%e a(1) = 5: {1,2,3,4,5,6,7,8,10}, {1,2,3,4,5,6,8,9,10}, {1,2,3,4,6,7,8,9,10}, {1,2,4,5,6,7,8,9,10}, {2,3,4,5,6,7,8,9,10}.
%t LinearRecurrence[{5,-5,-15,35,1,-65,45,45,-65,1,35,-15,-5,5,-1},{0,5,25,110,350,1001,2485,5720,12120,24310,46126,83980,146860,248710,408430},40] (* _Harvey P. Dale_, Jun 10 2018 *)
%o (PARI) concat(0, Vec(x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^10) + O(x^30))) \\ _Colin Barker_, Feb 06 2017
%Y Column k=9 of A282011.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Feb 05 2017
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