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

0,2

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.

Links

Table of n, a(n) for n=0..54.

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

Cf. A037965

Sequence in context: A265783 A246670 A075095 * A156136 A134243 A182779

Adjacent sequences: A178340 A178341 A178342 * A178344 A178345 A178346

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