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URL: https://oeis.org/A114968

⇱ A114968 - OEIS

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A114968
a(n) = floor(n^(n/6)/n!!!!!!).
0
1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 6, 4, 4, 5, 7, 10, 15, 11, 12, 14, 18, 26, 37, 28, 29, 35, 46, 64, 94, 71, 74, 89, 117, 163, 238, 180, 188, 226, 297, 416, 608, 461, 481, 580, 763, 1067, 1563, 1187, 1240, 1496, 1969, 2755, 4038, 3070
OFFSET
1,12
COMMENTS
This sequence is an approximation of a sextuple factorial analog to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 6, 8, 9, 12.
FORMULA
a(n) = floor(n^(n/6)/n!!!!!!). a(n) = floor(n^(n/6)/n!6). a(n) = floor((A000312(n)^(1/6))/A085158(n)).
EXAMPLE
a(12) = floor(12^2/12!!!!!) = floor(12^2/72) = floor(2) = 2.
a(18) = floor(18^3/18!!!!!) = floor((18^3)/1296) = floor(4.5) = 4.
a(24) = floor(24^4/20!!!!!) = floor((24^4)/31104) = floor(10.6666667) = 10.
a(30) = floor(30^5/25!!!!!) = floor((30^5)/933120) = floor(26.0416667) = 26.
a(36) = floor(36^6/30!!!!!) = floor((36^6)/33592320) = floor(64.8) = 64.
MATHEMATICA
fac[n_, m_] := Block[{t = n, f = Max[1, n]}, While[t > m, t -= m; f *= t]; f]; a[n_] := Floor[n^(n/6)/fac[n, 6]]; Array[a, 65] (* Giovanni Resta, Jun 15 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 22 2006
EXTENSIONS
Corrected and extended by Giovanni Resta, Jun 15 2016
STATUS
approved