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Number of n-element subsets of [n+10] having an even sum.
2

%I #6 Sep 18 2024 09:46:05

%S 1,5,30,146,511,1491,3976,9752,21942,46126,92252,176484,323554,571802,

%T 980232,1634776,2656511,4217499,6560554,10016006,15024009,22174581,

%U 32253936,46282704,65567164,91786604,127089144,174169352,236372692,317866884,423822512

%N Number of n-element subsets of [n+10] having an even sum.

%H Alois P. Heinz, <a href="/A282086/b282086.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (11, -61, 231, -675, 1617, -3287, 5797, -9002, 12430, -15362, 17062, -17062, 15362, -12430, 9002, -5797, 3287, -1617, 675, -231, 61, -11, 1).

%F G.f.: -(x^4-2*x^3+4*x^2-2*x+1) * (x^8-4*x^7+24*x^6-44*x^5+62*x^4-44*x^3 + 24*x^2-4*x+1) / ((x^2+1)^6*(x-1)^11).

%F a(n) = A282011(n+10,n).

%Y Cf. A282011.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Feb 05 2017