cp's OEIS Frontend

A182073 Square array read by antidiagonals: T(n,k) = n!*k! / (floor(n/2)! * floor(k/2)! * floor((n+k)/2)!).

%I A182073 #12 Aug 21 2017 03:14:42
%S A182073 1,1,1,2,1,2,6,2,2,6,6,3,2,3,6,30,6,6,6,6,30,20,10,4,6,4,10,20,140,20,
%T A182073 20,12,12,20,20,140,70,35,10,15,6,15,10,35,70,630,70,70,30,30,30,30,
%U A182073 70,70,630,252,126,28,42,12,30,12,42,28,126,252
%N A182073 Square array read by antidiagonals: T(n,k) = n!*k! / (floor(n/2)! * floor(k/2)! * floor((n+k)/2)!).
%C A182073 Compare with A068555 whose entries are given by (2*n)!*(2*k)!/(n!*k!*(n+k)!). See also A211226.
%H A182073 G. C. Greubel, <a href="/A182073/b182073.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A182073 That T(n,k) is an integer follows from the formulas:
%F A182073 T(2*n,2*k) = (2*n)!*(2*k)!/(n!*k!*(n+k)!) = A068555(n,k);
%F A182073 T(2*n,2*k+1) = (2*n)!*(2*k+1)!/(n!*k!*(n+k)!) = (2*k+1)*A068555(n,k);
%F A182073 T(2*n+1,2*k) = (2*n+1)!*(2*k)!/(n!*k!*(n+k)!) = (2*n+1)*A068555(n,k);
%F A182073 T(2*n+1,2*k+1) = (2*n+1)!*(2*k+1)!/(n!*k!*(n+k+1)!) = (2*k+1)*A135573(n,k).
%e A182073 As a square array
%e A182073 .n\k.|...0....1....2....3....4....5....6...
%e A182073 = = = = = = = = = = = = = = = = = = = = = =
%e A182073 ..0..|...1....1....2....6....6...30...20...
%e A182073 ..1..|...1....1....2....3....6...10...20...
%e A182073 ..2..|...2....2....2....6....4...20...10...
%e A182073 ..3..|...6....3....6....6...12...15...30...
%e A182073 ..4..|...6....6....4...12....6...30...12...
%e A182073 ..5..|..30...10...20...15...30...30...60...
%e A182073 ..6..|..20...20...10...30...12...60...20...
%e A182073 ...
%e A182073 Formatted as a triangle
%e A182073 .n\k.|...0....1....2....3....4....5....6
%e A182073 = = = = = = = = = = = = = = = = = = = = =
%e A182073 ..0..|...1
%e A182073 ..1..|...1....1
%e A182073 ..2..|...2....1....2
%e A182073 ..3..|...6....2....2....6
%e A182073 ..4..|...6....3....2....3....6
%e A182073 ..5..|..30....6....6....6....6...30
%e A182073 ..6..|..20...10....4....6....4...10...20
%e A182073 ...
%t A182073 T[n_, k_] := n!*k!/(Floor[n/2]!*Floor[k/2]!*Floor[(n + k)/2]!);
%t A182073 TableForm[Table[T[n, k], {n, 0, 5}, {k, 0, 10}]]
%t A182073 Table[T[n - k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* _G. C. Greubel_, Aug 20 2017 *)
%Y A182073 Cf. A068555, A135573, A211226.
%K A182073 nonn,easy,tabl
%O A182073 0,4
%A A182073 _Peter Bala_, Apr 10 2012