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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).
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%I #5 Oct 12 2012 14:54:49

%S 9,42,42,120,196,120,270,560,560,270,525,1260,1600,1260,525,924,2450,

%T 3600,3600,2450,924,1512,4312,7000,8100,7000,4312,1512,2340,7056,

%U 12320,15750,15750,12320,7056,2340,3465,10920,20160,27720,30625,27720,20160

%N 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 Row sums with zeros:

%C {0, 0, 9, 84, 436, 1660, 5170, 13948, 33748}.

%D 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 f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1).

%e Initial Zeros removed:

%e {9},

%e {42, 42},

%e {120, 196, 120},

%e {270, 560, 560, 270},

%e {525, 1260, 1600, 1260, 525},

%e {924, 2450, 3600, 3600, 2450, 924},

%e {1512, 4312, 7000, 8100, 7000, 4312, 1512},

%e {2340, 7056, 12320, 15750, 15750, 12320, 7056, 2340},

%e {3465, 10920, 20160, 27720, 30625, 27720, 20160, 10920, 3465}

%t 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 Cf. A117662.

%K nonn,tabl

%O 1,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 25 2008