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%I #3 Jan 19 2019 04:15:43
%S 1,3,2,12,8,60,40,24,360,240,144,2520,1680,1008,720,20160,13440,8064,
%T 5760,181440,120960,72576,51840,1814400,1209600,725760,518400,
%U 19958400,13305600,7983360,5702400,3628800,239500800,159667200,95800320,68428800
%N Triangular sequence based on A002301 and the alternating groups a prime -adic: t(n,m)=n!/Prime[m] for n>=Prime[m].
%C 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]
%F t(n,m)=n!/Prime[m] for n>=Prime[m]
%e {1},
%e {3, 2},
%e {12, 8},
%e {60, 40, 24},
%e {360, 240, 144},
%e {2520, 1680, 1008, 720},
%e {20160, 13440, 8064, 5760},
%e {181440, 120960, 72576, 51840},
%e {1814400, 1209600, 725760, 518400},
%t 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]
%Y Cf. A002301.
%K nonn,tabl,uned
%O 1,2
%A _Roger L. Bagula_, Jun 06 2007
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