%I
%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(n1) + d where d is the sum of the absolute differences between all pairs of previous terms.
%F a(n) = a(n1) + sum_{1<=i<j<n} (a(j)a(i))
%F a(n) = (n+1)(a(n1)a(n2)) + a(n3) 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 (21) + (31) + (71) + (32) + (72) + (73) = 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[n1]a[n2])+a[n3]
%K nonn
%O 1,2
%A _Amarnath Murthy_, Nov 14 2003
%E Edited by _Dean Hickerson_ and _Ray Chandler_, Nov 15 2003
