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A093420 Triangle read by rows: T(n,k) is the numerator of f(n, k) = (Product_{i = 0..k-1} (n-i))/(Sum_{i = 1..k} i) for 1 <= k <= n.

%I A093420 #19 Oct 22 2019 04:20:49
%S A093420 1,2,2,3,2,1,4,4,4,12,5,20,10,12,8,6,10,20,36,48,240,7,14,35,84,168,
%T A093420 240,180,8,56,56,168,448,960,1440,1120,9,24,84,1512,1008,2880,6480,
%U A093420 10080,8064,10,30,120,504,2016,7200,21600,50400,80640,725760,11,110,165
%N A093420 Triangle read by rows: T(n,k) is the numerator of f(n, k) = (Product_{i = 0..k-1} (n-i))/(Sum_{i = 1..k} i) for 1 <= k <= n.
%F A093420 T(n,n) = numerator(f(n, n)) = numerator(2*(n-1)!/(n+1)) = A090586(n).
%e A093420 Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
%e A093420   1,
%e A093420   2,  2,
%e A093420   3,  2,  1,
%e A093420   4,  4,  4, 12,
%e A093420   5, 20, 10, 12,   8,
%e A093420   6, 10, 20, 36,  48, 240,
%e A093420   7, 14, 35, 84, 168, 240, 180;
%e A093420   ...
%Y A093420 Cf. A090585, A090586, A093412, A093421 (denominators), A093422.
%K A093420 nonn,easy,frac,tabl,less
%O A093420 1,2
%A A093420 _Amarnath Murthy_, Mar 30 2004
%E A093420 Edited and extended by _David Wasserman_, Aug 29 2006