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

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

Author

Roger L. Bagula, May 25 2010

Keywords

• nonn
• easy
• tabl

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.

Examples

			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;
		

Crossrefs

Cf. A037965

Programs

Mathematica

Flatten[Table[Table[Binomial[n, m]/Beta[m + 1, n - m + 1], {m, 0, n}], {n, 0, 10}]]

Formula

T(n,m)=T(n,n-m) = (n+1)*( binomial(n,m))^2 = (n+1)*A008459(n).

Extensions

Edited by the Assoc. Eds. of the OEIS - Jun 27 2010