A129915 Triangular sequence of when integers are of the form: factorial[n]=a(n)*2^m ;Sequence dividing the powers of two out of factorials.

1, 1, 1, 2, 3, 6, 3, 6, 12, 24, 15, 30, 60, 120, 45, 90, 180, 360, 720, 315, 630, 1260, 2520, 5040, 315, 630, 1260, 2520, 5040, 10080, 20160, 40320, 2835, 5670, 11340, 22680, 45360, 90720, 181440, 362880, 14175, 28350, 56700, 113400, 226800, 453600

Offset

1,4

Comments

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}

Links

Table of n, a(n) for n=1..46.

Formula

t(n,m) = If Integer( n!/2^m)

Example

{1},
{1},
{1, 2},
{3, 6},
{3, 6, 12, 24},
{15, 30, 60, 120},
{45, 90, 180,360, 720},
{315, 630, 1260, 2520, 5040},
{315, 630, 1260, 2520, 5040, 10080, 20160, 40320}

Mathematica

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]

Crossrefs

Cf. A049606, A067655.

Sequence in context: A245499 A323642 A193898 * A019773 A350728 A109536

Adjacent sequences: A129912 A129913 A129914 * A129916 A129917 A129918

Keyword

nonn,uned,tabl

Author

Roger L. Bagula, Jun 05 2007

Status

approved