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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). 0
 9, 42, 42, 120, 196, 120, 270, 560, 560, 270, 525, 1260, 1600, 1260, 525, 924, 2450, 3600, 3600, 2450, 924, 1512, 4312, 7000, 8100, 7000, 4312, 1512, 2340, 7056, 12320, 15750, 15750, 12320, 7056, 2340, 3465, 10920, 20160, 27720, 30625, 27720, 20160 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums with zeros: {0, 0, 9, 84, 436, 1660, 5170, 13948, 33748}. REFERENCES 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. LINKS FORMULA f(n)=n*(n - 1)*(n - 2)*(n + 3)/12; t(n,m)=f(n - m + 1)*f(m + 1). EXAMPLE Initial Zeros removed: {9}, {42, 42}, {120, 196, 120}, {270, 560, 560, 270}, {525, 1260, 1600, 1260, 525}, {924, 2450, 3600, 3600, 2450, 924}, {1512, 4312, 7000, 8100, 7000, 4312, 1512}, {2340, 7056, 12320, 15750, 15750, 12320, 7056, 2340}, {3465, 10920, 20160, 27720, 30625, 27720, 20160, 10920, 3465} MATHEMATICA 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[%] CROSSREFS Cf. A117662. Sequence in context: A235642 A050635 A065792 * A075233 A062783 A172464 Adjacent sequences:  A118543 A118544 A118545 * A118547 A118548 A118549 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Aug 25 2008 STATUS approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)