cp's OEIS Frontend

A360858 Triangle read by rows. T(n, k) = binomial(n + 1, ceil(k/2)) * binomial(n, floor(k/2)).

%I A360858 #12 Feb 28 2023 10:03:55
%S A360858 1,1,2,1,3,6,1,4,12,18,1,5,20,40,60,1,6,30,75,150,200,1,7,42,126,315,
%T A360858 525,700,1,8,56,196,588,1176,1960,2450,1,9,72,288,1008,2352,4704,7056,
%U A360858 8820,1,10,90,405,1620,4320,10080,17640,26460,31752
%N A360858 Triangle read by rows. T(n, k) = binomial(n + 1, ceil(k/2)) * binomial(n, floor(k/2)).
%e A360858 Triangle T(n, k) starts:
%e A360858 [0] 1;
%e A360858 [1] 1,  2;
%e A360858 [2] 1,  3,  6;
%e A360858 [3] 1,  4, 12,  18;
%e A360858 [4] 1,  5, 20,  40,   60;
%e A360858 [5] 1,  6, 30,  75,  150,  200;
%e A360858 [6] 1,  7, 42, 126,  315,  525,   700;
%e A360858 [7] 1,  8, 56, 196,  588, 1176,  1960,  2450;
%e A360858 [8] 1,  9, 72, 288, 1008, 2352,  4704,  7056,  8820;
%e A360858 [9] 1, 10, 90, 405, 1620, 4320, 10080, 17640, 26460, 31752.
%p A360858 A360858 := (n, k) -> binomial(n + 1, ceil(k/2))*binomial(n, floor(k/2)):
%p A360858 seq(seq(A360858(n, k), k = 0..n), n = 0..9);
%o A360858 (Python)
%o A360858 from math import comb
%o A360858 def A360858_T(n,k): return comb(n,m:=k>>1)**2*(n+1)//(m+1 if k&1 else n+1-m) # _Chai Wah Wu_, Feb 28 2023
%Y A360858 Cf. A005566 (main diagonal), A001700 (row sums).
%Y A360858 Cf. A360857, A360859.
%K A360858 nonn,tabl
%O A360858 0,3
%A A360858 _Peter Luschny_, Feb 28 2023