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A178343 Triangle T(n,m)= binomial(n, m)/Beta(m + 1, n - m + 1) read by rows.

%I A178343 #2 Mar 30 2012 17:34:41
%S A178343 1,2,2,3,12,3,4,36,36,4,5,80,180,80,5,6,150,600,600,150,6,7,252,1575,
%T A178343 2800,1575,252,7,8,392,3528,9800,9800,3528,392,8,9,576,7056,28224,
%U A178343 44100,28224,7056,576,9,10,810,12960,70560,158760,158760,70560,12960,810,10
%N A178343 Triangle T(n,m)= binomial(n, m)/Beta(m + 1, n - m + 1) read by rows.
%C A178343 Beta(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y) is the Beta-function.
%C A178343 Row sums are A037965(n+1). The second column is A011379.
%F A178343 T(n,m)=T(n,n-m) = (n+1)*( binomial(n,m))^2 = (n+1)*A008459(n).
%e A178343 1;
%e A178343 2, 2;
%e A178343 3, 12, 3;
%e A178343 4, 36, 36, 4;
%e A178343 5, 80, 180, 80, 5;
%e A178343 6, 150, 600, 600, 150, 6;
%e A178343 7, 252, 1575, 2800, 1575, 252, 7;
%e A178343 8, 392, 3528, 9800, 9800, 3528, 392, 8;
%e A178343 9, 576, 7056, 28224, 44100, 28224, 7056, 576, 9;
%e A178343 10, 810, 12960, 70560, 158760, 158760, 70560, 12960, 810, 10;
%e A178343 11, 1100, 22275, 158400, 485100, 698544, 485100, 158400, 22275, 1100, 11;
%t A178343 Flatten[Table[Table[Binomial[n, m]/Beta[m + 1, n - m + 1], {m, 0, n}], {n, 0, 10}]]
%Y A178343 Cf. A037965
%K A178343 nonn,easy,tabl
%O A178343 0,2
%A A178343 _Roger L. Bagula_, May 25 2010
%E A178343 Edited by the Assoc. Eds. of the OEIS - Jun 27 2010