Voozh

VOOZH

URL: https://oeis.org/A178343

⇱ A178343 - OEIS

login

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

(list; table; graph; refs; listen; history; text; internal format)

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

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