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A178343
Triangle T(n,m)= binomial(n, m)/Beta(m + 1, n - m + 1) read by rows.
0
1, 2, 2, 3, 12, 3, 4, 36, 36, 4, 5, 80, 180, 80, 5, 6, 150, 600, 600, 150, 6, 7, 252, 1575, 2800, 1575, 252, 7, 8, 392, 3528, 9800, 9800, 3528, 392, 8, 9, 576, 7056, 28224, 44100, 28224, 7056, 576, 9, 10, 810, 12960, 70560, 158760, 158760, 70560, 12960, 810, 10
OFFSET
0,2
COMMENTS
Beta(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y) is the Beta-function.
Row sums are A037965(n+1). The second column is A011379.
FORMULA
T(n,m)=T(n,n-m) = (n+1)*( binomial(n,m))^2 = (n+1)*A008459(n).
EXAMPLE
1;
2, 2;
3, 12, 3;
4, 36, 36, 4;
5, 80, 180, 80, 5;
6, 150, 600, 600, 150, 6;
7, 252, 1575, 2800, 1575, 252, 7;
8, 392, 3528, 9800, 9800, 3528, 392, 8;
9, 576, 7056, 28224, 44100, 28224, 7056, 576, 9;
10, 810, 12960, 70560, 158760, 158760, 70560, 12960, 810, 10;
11, 1100, 22275, 158400, 485100, 698544, 485100, 158400, 22275, 1100, 11;
MATHEMATICA
Flatten[Table[Table[Binomial[n, m]/Beta[m + 1, n - m + 1], {m, 0, n}], {n, 0, 10}]]
CROSSREFS
Sequence in context: A265783 A246670 A075095 * A156136 A134243 A182779
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula, May 25 2010
EXTENSIONS
Edited by the Assoc. Eds. of the OEIS - Jun 27 2010
STATUS
approved