|
Search: id:A079478
|
|
|
| A079478 |
|
Coefficient of x^0 in P(n,x) = prod(i=0,n-1,i!^2)/matdet(M(n)) of degree n^2 where M(n) is the n X n matrix m(i,j)=1/(i+j+x). |
|
+0
6
|
|
| 1, 2, 72, 172800, 60963840000, 5574884681318400000, 205619158526859285626880000000, 4394314874750658447092552646524928000000000
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Product of all matrix elements of n X n matrix M(i,j) = i+j (i,j=1..n). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
|
|
FORMULA
|
a(n)=(n+1)*prod(i=0, n, (n+i)!)/prod(i=1, n+1, i!)
a(n) =A000178(2n)/A000178(n)^2, i.e. "central supercombinations" by analogy with A000984. - Henry Bottomley (se16(AT)btinternet.com), May 14 2005
a(n) = Product[Product[(i+j),{i,1,n}],{j,1,n}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
|
|
EXAMPLE
|
determinant of M(2) is 1/(x^4 + 12*x^3 + 53*x^2 + 102*x + 72) hence a(2)=72
|
|
MAPLE
|
seq(mul(mul(k+j, j=1..n), k=1..n), n=0..8); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 01 2007
|
|
MATHEMATICA
|
Table[Product[Product[(i+j), {i, 1, n}], {j, 1, n}], {n, 0, 10}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
|
|
PROGRAM
|
(PARI) a(n)=(n+1)*prod(i=0, n, (n+i)!)/prod(i=1, n+1, i!)
|
|
CROSSREFS
|
Cf. A011379.
Central column in triangle A009963.
Sequence in context: A099681 A062082 A067689 this_sequence A036899 A041647 A083018
Adjacent sequences: A079475 A079476 A079477 this_sequence A079479 A079480 A079481
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 15 2003
|
|
|
Search completed in 0.002 seconds
|
