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a(n) = binomial(n, floor(n/2)) - n*(n - 1)/2.
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%I #9 Sep 21 2024 02:29:48

%S 1,1,0,0,0,5,14,42,90,207,407,858,1638,3341,6330,12750,24174,48467,

%T 92207,184566,352506,705201,1351825,2703880,5200000,10400275,20057949,

%U 40116222,77558354,155117085,300539730,601079894,1166802582,2333605659,4537567055,9075134670,17672631234,35345263097,68923263669,137846528040,269128936400,538257873579

%N a(n) = binomial(n, floor(n/2)) - n*(n - 1)/2.

%F a(n) = binomial(n, floor(n/2)) - n*(n - 1)/2 = A001405(n) - A000217(n-1).

%t a[n_] = Binomial[n, Floor[n/2]] - n*(n - 1)/2; Table[a[n], {n, 1, 30}]

%Y Cf. A000217, A001405.

%K nonn,less,easy

%O 1,6

%A _Roger L. Bagula_, Jun 09 2007