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A360859 Triangle read by rows. T(n, k) = binomial(n, ceil(k/2)) * binomial(n, floor(k/2)).

%I A360859 #11 Feb 28 2023 09:46:38
%S A360859 1,1,1,1,2,4,1,3,9,9,1,4,16,24,36,1,5,25,50,100,100,1,6,36,90,225,300,
%T A360859 400,1,7,49,147,441,735,1225,1225,1,8,64,224,784,1568,3136,3920,4900,
%U A360859 1,9,81,324,1296,3024,7056,10584,15876,15876,1,10,100,450,2025,5400,14400,25200,44100,52920,63504
%N A360859 Triangle read by rows. T(n, k) = binomial(n, ceil(k/2)) * binomial(n, floor(k/2)).
%e A360859 Triangle T(n, k) starts:
%e A360859 [0] 1;
%e A360859 [1] 1, 1;
%e A360859 [2] 1, 2,  4;
%e A360859 [3] 1, 3,  9,   9;
%e A360859 [4] 1, 4, 16,  24,   36;
%e A360859 [5] 1, 5, 25,  50,  100,  100;
%e A360859 [6] 1, 6, 36,  90,  225,  300,  400;
%e A360859 [7] 1, 7, 49, 147,  441,  735, 1225,  1225;
%e A360859 [8] 1, 8, 64, 224,  784, 1568, 3136,  3920,  4900;
%e A360859 [9] 1, 9, 81, 324, 1296, 3024, 7056, 10584, 15876, 15876;
%p A360859 A360859 := (n, k) -> binomial(n, ceil(k/2)) * binomial(n, floor(k/2)):
%p A360859 seq(seq(A360859(n, k), k = 0..n), n = 0..10);
%o A360859 (Python)
%o A360859 from math import comb
%o A360859 def A360859_T(n,k): return comb(n,m:=k>>1)**2*(n-m)//(m+1) if k&1 else comb(n,k>>1)**2 # _Chai Wah Wu_, Feb 28 2023
%Y A360859 Cf. A018224 (main diagonal), A360861 (row sums).
%Y A360859 Cf. A360857, A360858.
%K A360859 nonn,tabl
%O A360859 0,5
%A A360859 _Peter Luschny_, Feb 28 2023