This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282085 #12 Sep 18 2024 09:45:07
%S A282085 1,5,25,110,365,1001,2485,5720,12190,24310,46126,83980,147070,248710,
%T A282085 408430,653752,1021735,1562275,2343055,3453450,5008003,7153575,
%U A282085 10079355,14024400,19284460,26225628,35302540,47071640,62203340,81505820,105955628,136719440
%N A282085 Number of n-element subsets of [n+9] having an even sum.
%H A282085 Alois P. Heinz, <a href="/A282085/b282085.txt">Table of n, a(n) for n = 0..1000</a>
%H A282085 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (10, -50, 170, -445, 952, -1720, 2680, -3650, 4380, -4652, 4380, -3650, 2680, -1720, 952, -445, 170, -50, 10, -1).
%F A282085 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)^10).
%F A282085 a(n) = A282011(n+9,n).
%e A282085 a(0) = 1: {}.
%e A282085 a(1) = 5: {2}, {4}, {6}, {8}, {10}.
%e A282085 a(2) = 25: {1,3}, {1,5}, {1,7}, {1,9}, {1,11}, {2,4}, {2,6}, {2,8}, {2,10}, {3,5}, {3,7}, {3,9}, {3,11}, {4,6}, {4,8}, {4,10}, {5,7}, {5,9}, {5,11}, {6,8}, {6,10}, {7,9}, {7,11}, {8,10}, {9,11}.
%t A282085 T[n_, k_] := Sum[Binomial[Ceiling[n/2], 2 j] Binomial[Floor[n/2], k - 2 j], {j, 0, Floor[(n + 1)/4]}]; Table[T[n + 9, n], {n, 0, 31}] (* or *) CoefficientList[Series[(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)^10), {x, 0, 31}], x] (* _Indranil Ghosh_, Feb 26 2017 *)
%Y A282085 Cf. A282011.
%K A282085 nonn,easy
%O A282085 0,2
%A A282085 _Alois P. Heinz_, Feb 05 2017