A129925 Triangular sequence based on A002301 and the alternating groups a prime -adic: t(n,m)=n!/Prime[m] for n>=Prime[m].

1, 3, 2, 12, 8, 60, 40, 24, 360, 240, 144, 2520, 1680, 1008, 720, 20160, 13440, 8064, 5760, 181440, 120960, 72576, 51840, 1814400, 1209600, 725760, 518400, 19958400, 13305600, 7983360, 5702400, 3628800, 239500800, 159667200, 95800320, 68428800

Offset: 1

Author

Roger L. Bagula, Jun 06 2007

Keywords

• nonn
• tabl
• uned

Comments

Alternating groups are: An->n!/2 for n>=2 If the tritonic or triple symmetric groups are: Tn->n!/3 for n>=4 Then the pentatonic would be: Pn->n!/5 for n>=5 General: ( triangular sequence) G(m)n=n!/Prime[m] for n>=Prime[m]

Examples

			{1},
{3, 2},
{12, 8},
{60, 40, 24},
{360, 240, 144},
{2520, 1680, 1008, 720},
{20160, 13440, 8064, 5760},
{181440, 120960, 72576, 51840},
{1814400, 1209600, 725760, 518400},
		

Crossrefs

Cf. A002301.

Programs

Mathematica

g[n_, m_] = If[n >= Prime[m], n!/Prime[m], {}]; a = Table[Flatten[Table[g[n, m], {m, 1, n}]], {n, 1, 23}]; Flatten[a]

Formula

t(n,m)=n!/Prime[m] for n>=Prime[m]