A141600 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))).

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, 14, 14, 14, 14, 10, 1, 1, 10, 17, 18, 20, 18, 17, 10, 1, 1, 11, 20, 24, 28, 28, 24, 20, 11, 1, 1, 12, 24, 31, 40, 43, 40, 31, 24, 12, 1

Offset

1,5

Comments

Row sums are {1, 2, 8, 18, 28, 38, 55, 78, 112, 168, 259, ...}.

The constant that is Exp[1]-like associated with the permutations is:

N[Sum[1/f[n], {n, 0, 255}]]=2.190669247268157.

Links

Table of n, a(n) for n=1..66.

Formula

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))).

Example

{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, 14, 14, 14, 14, 10, 1},
{1, 10, 17, 18, 20, 18, 17, 10, 1},
{1, 11, 20, 24, 28, 28, 24, 20, 11, 1},
{1, 12, 24, 31, 40, 43, 40, 31, 24, 12, 1}

Mathematica

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[%]

Crossrefs

Sequence in context: A171147 A171695 A179233 * A303489 A195408 A011491

Adjacent sequences: A141597 A141598 A141599 * A141601 A141602 A141603

Keyword

nonn,uned,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 21 2008

Status

approved