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%I #10 Apr 07 2013 02:49:44
%S 1,112,7896,453056,23232176,1113673728,51155215360,2284897159168,
%T 100157064553728,4334351404617728,185915811851773952,
%U 7925465707325177856,336395829865869340672,14234737653310804590592
%N Sixth column of the triangle A071951 (Legendre-Stirling).
%F G.f.: 1/product(1- p*(p+1)*x, p=1..6).
%F a(n)= A071951(n+6, 6), n>=0.
%F a(n)= sum(A089278(6, p)*(p*(p+1))^n, p=1..6)/A089500(6)= (-11*2^n + 7425*6^n - 266112*12^n + 2000000*20^n - 4640625*30^n + 3176523*42^n)/277200.
%F a(n) = det(|ps(i+6,j+5)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). [_Mircea Merca_, Apr 06 2013]
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Nov 07 2003