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A118546 A symmetrical triangle of coefficient weights: A117662 :f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1).

%I A118546 #5 Oct 12 2012 14:54:49
%S A118546 9,42,42,120,196,120,270,560,560,270,525,1260,1600,1260,525,924,2450,
%T A118546 3600,3600,2450,924,1512,4312,7000,8100,7000,4312,1512,2340,7056,
%U A118546 12320,15750,15750,12320,7056,2340,3465,10920,20160,27720,30625,27720,20160
%N A118546 A symmetrical triangle of coefficient weights: A117662 :f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1).
%C A118546 Row sums with zeros:
%C A118546 {0, 0, 9, 84, 436, 1660, 5170, 13948, 33748}.
%D A118546 Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, Inc., New York, 1972, page145: Number of algebraic scalars constructed from curvature R(i,j,k,l) and metric ground form g(i,j):A117662.
%F A118546 f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1).
%e A118546 Initial Zeros removed:
%e A118546 {9},
%e A118546 {42, 42},
%e A118546 {120, 196, 120},
%e A118546 {270, 560, 560, 270},
%e A118546 {525, 1260, 1600, 1260, 525},
%e A118546 {924, 2450, 3600, 3600, 2450, 924},
%e A118546 {1512, 4312, 7000, 8100, 7000, 4312, 1512},
%e A118546 {2340, 7056, 12320, 15750, 15750, 12320, 7056, 2340},
%e A118546 {3465, 10920, 20160, 27720, 30625, 27720, 20160, 10920, 3465}
%t A118546 f[n_] = n*(n - 1)*(n - 2)*(n + 3)/12; t[n_, m_] = f[n - m + 1]*f[m + 1]; Table[Table[t[n, m], {m, 2, n - 2}], {n, 2, 12}]; Flatten[%]
%Y A118546 Cf. A117662.
%K A118546 nonn,tabl
%O A118546 1,1
%A A118546 _Roger L. Bagula_ and _Gary W. Adamson_, Aug 25 2008