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Search: id:A141601
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| A141601 |
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A neo-combination triangle of coefficients based on the renormalization of permutations by the SO(n) or (D_2*n-1,B_2*n) group element numbers: a(n)=n*(n-1)/2; f(n)=n*f(n-1)*a(n)/a(n-1); t(n,m)=Round( f(n)/(f(n-m)*f(m))). |
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1
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| 1, 1, 1, 1, 2, 1, 1, 9, 9, 1, 1, 8, 36, 8, 1, 1, 8, 33, 33, 8, 1, 1, 9, 38, 33, 38, 9, 1, 1, 10, 44, 41, 41, 44, 10, 1, 1, 11, 52, 52, 54, 52, 52, 11, 1, 1, 12, 62, 67, 76, 76, 67, 62, 12, 1, 1, 12, 72, 86, 105, 113, 105, 86, 72, 12, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 4, 20, 54, 84, 129, 192, 286, 436, 665};
The constant that is Exp[1]-like associated with the permutations is:
N[Sum[1/f[n], {n, 0, 255}]]=2.5634363430819094.
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FORMULA
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a(n)=n*(n-1)/2; f(n)=n*f(n-1)*a(n)/a(n-1); t(n,m)=Round( f(n)/(f(n-m)*f(m))).
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 9, 9, 1},
{1, 8, 36, 8, 1},
{1, 8, 33, 33, 8, 1},
{1, 9, 38, 33, 38, 9, 1},
{1, 10, 44, 41, 41, 44, 10, 1},
{1, 11, 52, 52, 54, 52, 52, 11, 1},
{1, 12, 62, 67, 76, 76, 67, 62, 12, 1},
{1, 12, 72, 86, 105, 113, 105, 86, 72, 12, 1}
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MATHEMATICA
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Clear[a, f, t, n, m]; a[0] = 1; a[1] = 1; a[n_] := a[n] = n*(n-1)/2; 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[%]
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CROSSREFS
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Sequence in context: A016540 A132620 A019803 this_sequence A108558 A128434 A119731
Adjacent sequences: A141598 A141599 A141600 this_sequence A141602 A141603 A141604
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Aug 21 2008
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