%I A059332
%S A059332 1,2,24,3456,9953280,859963392000,3120635156889600000,
%T A059332 634153008009974906880000000,9278496603801318870491332608000000000,
%U A059332 12218100099725239100847669366019325952000000000000
%N A059332 Determinant of n X n matrix A defined by A[i,j] = (i+j-1)! for 1 <= i,
j <= n.
%C A059332 Hankel transform of n! (A000142(n)) and of A003319. [From Paul Barry
(pbarry(AT)wit.ie), Oct 07 2008]
%C A059332 Hankel transform of A000255. [From Paul Barry (pbarry(AT)wit.ie), Apr
22 2009]
%F A059332 a(n) = a(n-1)*(n!)*(n-1)! for n >= 2 so a(n) = product k=1, 2, ..., n
k!*(k-1)!
%F A059332 a(n)=2^C(n,2)*product{k=1..(n-1), C(k+2,2)^(n-1-k)}. [From Paul Barry
(pbarry(AT)wit.ie), Jan 15 2009]
%F A059332 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27
2009: (Start)
%F A059332 a(n) = n!*product(k!, k=0..n-1)^2
%F A059332 (End)
%e A059332 a(4) = 3456 because the relevant matrix is {1 2 6 24 / 2 6 24 120 / 6
24 120 720 / 24 120 720 5040 } and the determinant is 3456.
%p A059332 with(linalg): Digits := 500: A059332 := proc(n) local A, i, j: A := array(1..n,
1..n): for i from 1 to n do for j from 1 to n do A[i,j] := (i+j-1)!
od: od: RETURN(det(A)) end: for n from 1 to 20 do printf(`%d,`, A059332(n))
od;
%Y A059332 Cf. A010790.
%Y A059332 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27
2009: (Start)
%Y A059332 Cf. A162014 and A055209.
%Y A059332 (End)
%Y A059332 Sequence in context: A111428 A111429 A111430 this_sequence A000794 A159907
A088912
%Y A059332 Adjacent sequences: A059329 A059330 A059331 this_sequence A059333 A059334
A059335
%K A059332 nonn,easy
%O A059332 1,2
%A A059332 Noam Katz (noamkj(AT)hotmail.com), Jan 26 2001
%E A059332 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 29 2001
%E A059332 Offset corrected. Comment and formula aligned with new offset by Johannes
W. Meijer (meijgia(AT)hotmail.com), Jun 24 2009
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