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%I #25 Oct 21 2018 13:48:45
%S 1,1,1,1,1,1,1,2,2,1,1,2,4,2,1,1,3,6,6,3,1,1,4,12,12,12,4,1,1,5,20,30,
%T 30,20,5,1,1,6,30,60,90,60,30,6,1,1,8,48,120,240,240,120,48,8,1,1,10,
%U 80,240,600,800,600,240,80,10,1
%N Triangle read by rows: T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)).
%C Row sums are 1, 2, 3, 6, 10, 20, 46, 112, 284, 834, 2662, ... .
%H Donald E. Knuth and Herbert S. Wilf, <a href="http://www.math.upenn.edu/~wilf/website/dm36.pdf">The power of a prime that divides a generalized binomial coefficient</a>, J. Reine Angew. Math., 396:212-219, 1989.
%F T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)).
%F T(n,k) = Product_{i=1..n} A000009(i)/(Product_{i=1..k} A000009(i)*Product_{i=1..n-k} A000009(i)).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 2, 1;
%e 1, 2, 4, 2, 1;
%e 1, 3, 6, 6, 3, 1;
%e 1, 4, 12, 12, 12, 4, 1;
%e 1, 5, 20, 30, 30, 20, 5, 1;
%e 1, 6, 30, 60, 90, 60, 30, 6, 1;
%e 1, 8, 48, 120, 240, 240, 120, 48, 8, 1;
%e 1, 10, 80, 240, 600, 800, 600, 240, 80, 10, 1;
%t c[n_] := Product[PartitionsQ[m], {m, 1, n}];
%t t[n_, m_] := c[n]/(c[m]*c[n - m]);
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A000009, A152827.
%K nonn,tabl
%O 0,8
%A _Roger L. Bagula_, Feb 04 2010
%E New name and edits by _Tom Edgar_, Jan 23 2015
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