%I A067550
%S A067550 1,2,10,90,1260,25200,680400,23814000,1047816000,56582064000,
%T A067550 3677834160000,283193230320000,25487390728800000,2650688635795200000,
%U A067550 315431947659628800000,42583312934049888000000,6472663565975582976000000
%N A067550 (n-1)!(n+2)!/(3*2^n).
%C A067550 Determinant of n X n matrix whose diagonal are the first n triangular 
               numbers and all other elements are 1's.
%C A067550 a(n+1)/a(n) = A000096(n) = n(n+3)/2. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               May 20 2006
%e A067550 The determinant begins:
%e A067550 1 1 1 1 1 1 1 ...
%e A067550 1 3 1 1 1 1 1 ...
%e A067550 1 1 6 1 1 1 1 ...
%e A067550 1 1 1 10 1 1 1 ...
%e A067550 1 1 1 1 15 1 1 ...
%e A067550 1 1 1 1 1 21 1 ...
%t A067550 Table[ Det[ DiagonalMatrix[ Table[ i(i + 1)/2 - 1, {i, 1, n} ] ] + 1 
               ], {n, 1, 20} ]
%t A067550 Table[(n-1)!(n+2)!/3/2^n,{n,1,20}] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               May 20 2006
%Y A067550 Cf. A000096.
%Y A067550 Sequence in context: A060350 A096658 A055779 this_sequence A086587 A082472 
               A095937
%Y A067550 Adjacent sequences: A067547 A067548 A067549 this_sequence A067551 A067552 
               A067553
%K A067550 nonn
%O A067550 1,2
%A A067550 Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 28 2002