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%I #2 Mar 30 2012 17:34:21
%S 1,1,1,4,0,4,27,3,3,27,256,70,16,70,256,3125,1005,245,245,1005,3125,
%T 46656,15596,4112,1404,4112,15596,46656,823543,279895,78183,18487,
%U 18487,78183,279895,823543,16777216,5764746,1679776,397066,130944,397066
%N Symmetric triangular sequence of powers: t(n,m)=m^n + (n - m)^n - n*m*(n - m).
%C Row sum: Table[Apply[Plus, Table[t[n, m], {n, 0, m}]], {m, 0, 10}]; {1, 2, 8, 60, 668, 8750, 134132, 2400216, 49368552, 1148608890, 29828682200} ( not in OEIS either) Inspired by the necklace law: f(x,y,q)=x+y-q*x*y (C. Lenart: the family of formal group laws over the integers F_q(X,Y)=X+Y-qXY, q in Z: http://math.albany.edu:8000/math/pers/lenart/articles/fgl.html)
%F t(n,m)=m^n + (n - m)^n - n*m*(n - m) else if n=m=0, 1
%e {1},
%e {1, 1},
%e {4, 0, 4},
%e {27, 3, 3, 27},
%e {256, 70, 16, 70, 256},
%e {3125, 1005, 245, 245, 1005, 3125},
%e {46656, 15596, 4112, 1404, 4112, 15596, 46656}
%t t[m_, n_] = If [m == n == 0, 1, m^n + (n - m)^n - n*m*(n - m)]; aa = Table[Table[t[n, m], {n, 0, m}], {m, 0, 10}]; Flatten[aa]
%K nonn,uned
%O 1,4
%A _Roger L. Bagula_, Jun 08 2007
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