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A322127 Triangular array, read by rows: T(n,k) = numerator of binomial(n-1, n-k)/k!, 1 <= k <= n.

%I A322127 #21 Nov 28 2018 08:48:59
%S A322127 1,1,1,1,1,1,1,3,1,1,1,2,1,1,1,1,5,5,5,1,1,1,3,5,5,1,1,1,1,7,7,35,7,7,
%T A322127 1,1,1,4,14,7,7,7,1,1,1,1,9,6,7,21,7,1,1,1,1,1,5,15,5,7,7,1,1,1,1,1,1,
%U A322127 11,55,55,11,77,11,11,11,11,1,1,1,6,11,55,33,11,11,11,11,11,1,1,1
%N A322127 Triangular array, read by rows: T(n,k) = numerator of binomial(n-1, n-k)/k!, 1 <= k <= n.
%H A322127 Seiichi Manyama, <a href="/A322127/b322127.txt">Rows n = 1..140, flattened</a>
%e A322127 T(n,k) = binomial(n-1, n-k)/k!.
%e A322127 1/1;
%e A322127 1/1, 1/2;
%e A322127 1/1, 1/1, 1/6;
%e A322127 1/1, 3/2, 1/2,  1/24;
%e A322127 1/1, 2/1, 1/1,   1/6, 1/120;
%e A322127 1/1, 5/2, 5/3,  5/12,  1/24, 1/720;
%e A322127 1/1, 3/1, 5/2,   5/6,   1/8, 1/120, 1/5040;
%e A322127 1/1, 7/2, 7/2, 35/24,  7/24, 7/240,  1/720, 1/40320;
%t A322127 T[n_, k_] := Numerator[Binomial[n-1, n-k]/k!]; Table[T[n, k], {n,1,10}, {k,1,n}] // Flatten (* _Amiram Eldar_, Nov 27 2018 *)
%Y A322127 Cf. A007318, A322093, A322128.
%K A322127 nonn,frac,tabl,look
%O A322127 1,8
%A A322127 _Seiichi Manyama_, Nov 27 2018