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%I #5 Oct 12 2012 14:40:20
%S 1,4440,12715200,33158592000,84365452800000,213181366579200000,
%T 537634980016128000000,1355141067314135040000000,
%U 3415172150786516582400000000,8606389816065144913920000000000
%N Third column (k=7) sequence of array A090216 ((5,5)-Stirling2) divided by 600.
%F a(n)= A090216(n+2, 7)/600, n>=0.
%F a(n)= ((5!)^n)*(1-2*6^(n+1)+binomial(7, 2)^(n+1))/(2*5). From eq.12 of the Blasiak et al. reference given in A007840 with r=5=s, k=7.
%F a(n)= (21*(7*6*5*4*3)^n - 12*(6*5*4*3*2)^n + (5*4*3*2*1)^n)/10.
%F G.f.: (1+1080*x)/product(1-fallfac(p, 5)*x, p=5..7), with fallfac(n, m) := A008279(n, m) (falling factorials).
%Y Cf. A091553 (third column of array (4, 4)-Stirling2 divided by 72).
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Feb 13 2004
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