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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 A109536 A267352

Adjacent sequences:  A129912 A129913 A129914 * A129916 A129917 A129918

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Jun 05 2007

STATUS

approved

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Last modified September 18 15:58 EDT 2021. Contains 347527 sequences. (Running on oeis4.)