Search: id:A079478
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%I A079478
%S A079478 1,2,72,172800,60963840000,5574884681318400000,
%T A079478 205619158526859285626880000000,
%U A079478 4394314874750658447092552646524928000000000
%N 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).
%C A079478 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
%F A079478 a(n)=(n+1)*prod(i=0, n, (n+i)!)/prod(i=1, n+1, i!)
%F A079478 a(n) =A000178(2n)/A000178(n)^2, i.e. "central supercombinations" by analogy 
               with A000984. - Henry Bottomley (se16(AT)btinternet.com), May 14 
               2005
%F A079478 a(n) = Product[Product[(i+j),{i,1,n}],{j,1,n}]. - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Apr 12 2006
%e A079478 determinant of M(2) is 1/(x^4 + 12*x^3 + 53*x^2 + 102*x + 72) hence a(2)=72
%p A079478 seq(mul(mul(k+j,j=1..n), k=1..n), n=0..8); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 01 2007
%t A079478 Table[Product[Product[(i+j),{i,1,n}],{j,1,n}],{n,0,10}] - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Apr 12 2006
%o A079478 (PARI) a(n)=(n+1)*prod(i=0,n,(n+i)!)/prod(i=1,n+1,i!)
%Y A079478 Cf. A011379.
%Y A079478 Central column in triangle A009963.
%Y A079478 Sequence in context: A099681 A062082 A067689 this_sequence A036899 A041647 
               A083018
%Y A079478 Adjacent sequences: A079475 A079476 A079477 this_sequence A079479 A079480 
               A079481
%K A079478 nonn
%O A079478 0,2
%A A079478 Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 15 2003

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