%I #2 Mar 31 2012 20:17:50
%S 1,1,1,2,3,6,3,6,12,24,15,30,60,120,45,90,180,360,720,315,630,1260,
%T 2520,5040,315,630,1260,2520,5040,10080,20160,40320,2835,5670,11340,
%U 22680,45360,90720,181440,362880,14175,28350,56700,113400,226800,453600
%N Triangular sequence of when integers are of the form: factorial[n]=a(n)*2^m ;Sequence dividing the powers of two out of factorials.
%C A music scale like way of looking at symmetric and alternating group dimensions. Row sum is ( not in OEIS): Table[Apply[Plus, Reverse[Flatten[Table[If[IntegerQ[n!/2^m], n!/2^m, {}], {m, 0, n}]]]], {n, 0, 10}] {1, 1, 3, 9, 45, 225, 1395, 9765, 80325, 722925, 7243425} Also predicts a first row (minimum) sequence A049606: {1,1,3,3,15,45,315,315,2835,14175}
%F t(n,m) = If Integer( n!/2^m)
%e {1},
%e {1},
%e {1, 2},
%e {3, 6},
%e {3, 6, 12, 24},
%e {15, 30, 60, 120},
%e {45, 90, 180,360, 720},
%e {315, 630, 1260, 2520, 5040},
%e {315, 630, 1260, 2520, 5040, 10080, 20160, 40320}
%t f[n_, m_] := If[IntegerQ[n!/2^m], n!/2^m, {}]; a = Table[Reverse[Flatten[Table[If[IntegerQ[n!/2^m],n!/2^m, {}], {m, 0, n}]]], {n, 0, 10}]; Flatten[a]
%Y Cf. A049606, A067655.
%K nonn,uned,tabl
%O 1,4
%A _Roger L. Bagula_, Jun 05 2007