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%I #10 Jun 24 2014 01:08:36
%S 1,2,3,7,26,136,887,6785,59116,576528,6215729,73368729,940718528,
%T 13016462714,193285275705,3065510539375,51713071208774,
%U 924496937994286,17458742846249615,347270877144570683,7256791451501057782
%N a(1) = 1, a(2) = 2, a(n) = a(n-1) + d where d is the sum of the absolute differences between all pairs of previous terms.
%F a(n) = a(n-1) + sum_{1<=i<j<n} (a(j)-a(i))
%F a(n) = (n+1)(a(n-1)-a(n-2)) + a(n-3) for n>=5.
%F Conjecture: a(n) = c n! (1+2/n+(5/2)/n^2+(31/6)/n^3+(317/24)/n^4+O(1/n^5)), where c is about 0.1289432494744. - _Dean Hickerson_, Nov 15 2003
%F In closed form, c = BesselJ[3,2] = 0.128943249474402051... - _Vaclav Kotesovec_, Nov 19 2012
%e 26 follows 7 as the sum of the differences of previous terms is (2-1) + (3-1) + (7-1) + (3-2) + (7-2) + (7-3) = 19 and 7+19 = 26.
%t a[1]=1; a[2]=2; a[3]=3; a[4]=7; a[n_] := a[n]=(n+1)(a[n-1]-a[n-2])+a[n-3]
%K nonn
%O 1,2
%A _Amarnath Murthy_, Nov 14 2003
%E Edited by _Dean Hickerson_ and _Ray Chandler_, Nov 15 2003
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