|
Search: id:A061928
|
|
|
| A061928 |
|
Array T(n,m) = 1/beta(n+1,m+1) read by antidiagonals. |
|
+0
7
|
|
| 6, 12, 12, 20, 30, 20, 30, 60, 60, 30, 42, 105, 140, 105, 42, 56, 168, 280, 280, 168, 56, 72, 252, 504, 630, 504, 252, 72, 90, 360, 840, 1260, 1260, 840, 360, 90, 110, 495, 1320, 2310, 2772, 2310, 1320, 495, 110, 132, 660, 1980, 3960, 5544, 5544, 3960
(list; table; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
beta(n+1,m+1) = integral x^n * (1-x)^m dx from 0 to 1 for real n, m
|
|
REFERENCES
|
G. Boole, A Treatise On The Calculus of Finite Differences, Dover, 1960, p. 26.
|
|
FORMULA
|
beta(n+1, m+1) = gamma(n+1)*gamma(m+1)/gamma(n+m+2) = n!*m!/(n+m+1)!
|
|
EXAMPLE
|
Antidiagonals: 6, (12, 12), (20, 30, 20), (30, 60, 60, 30), ...
|
|
PROGRAM
|
(PARI) A(i, j)=if(i<1|j<1, 0, 1/subst(intformal(x^i*(1-x)^j), x, 1)) - Michael Somos Feb 05 2004.
(PARI) A(i, j)=if(i<1|j<1, 0, 1/sum(k=0, i, (-1)^k*binomial(i, k)/(j+1+k))) - Michael Somos Feb 05 2004.
|
|
CROSSREFS
|
Rows: 1/b(n, 2): A002378, 1/b(n, 3): A027480, 1/b(n, 4): A033488. Diagonals: 1/b(n, n): A002457, 1/b(n, n+1) A005430, 1/b(n, n+2): A000917.
T(i, j)=A003506(i+1, j+1).
Sequence in context: A135462 A156386 A129858 this_sequence A070149 A055595 A132632
Adjacent sequences: A061925 A061926 A061927 this_sequence A061929 A061930 A061931
|
|
KEYWORD
|
nonn,tabl,easy,nice
|
|
AUTHOR
|
Frank.Ellermann(AT)t-online.de, May 22 2001
|
|
|
Search completed in 0.002 seconds
|
