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%I #2 Oct 12 2012 14:54:51
%S 1,1,1,1,6,1,1,8,8,1,1,8,10,8,1,1,8,10,10,8,1,1,9,12,11,12,9,1,1,10,
%T 14,14,14,14,10,1,1,10,17,18,20,18,17,10,1,1,11,20,24,28,28,24,20,11,
%U 1,1,12,24,31,40,43,40,31,24,12,1
%N A neo-combination triangle of coefficients based on the renormalization of permutations by the SU(n) or A_n-1 group element numbers: a(n)=n^2-1; f(n)=n*f(n-1)*a(n)/a(n-1); t(n,m)=Round( f(n)/(f(n-m)*f(m))).
%C Row sums are {1, 2, 8, 18, 28, 38, 55, 78, 112, 168, 259, ...}.
%C The constant that is Exp[1]-like associated with the permutations is:
%C N[Sum[1/f[n], {n, 0, 255}]]=2.190669247268157.
%F a(n)=n^2-1; f(n)=n*f(n-1)*a(n)/a(n-1); t(n,m)=Round( f(n)/(f(n-m)*f(m))).
%e {1},
%e {1, 1},
%e {1, 6, 1},
%e {1, 8, 8, 1},
%e {1, 8, 10, 8, 1},
%e {1, 8, 10, 10, 8, 1},
%e {1, 9, 12, 11, 12, 9, 1},
%e {1, 10, 14, 14, 14, 14, 10, 1},
%e {1, 10, 17, 18, 20, 18, 17, 10, 1},
%e {1, 11, 20, 24, 28, 28, 24, 20, 11, 1},
%e {1, 12, 24, 31, 40, 43, 40, 31, 24, 12, 1}
%t Clear[a, f, t, n, m]; a[0] = 1; a[1] = 1; a[n_] := a[n] = n^2 - 1; Table[a[n], {n, 0, 20}]; f[0] = 1; f[1] = 1; f[n_] := f[n] = n*f[n - 1]*a[n]/a[n - 1]; Table[f[n], {n, 0, 20}]; t[n_, m_] := t[n, m] = f[n]/(f[n - m]*f[m]); Table[Table[Round[t[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%K nonn,uned,tabl
%O 1,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 21 2008
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