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A133799 a(2) = 1, a(3)=3; for n >= 4, a(n) = (n-2)!*Stirling_2(n,n-1)/2 = n!/4. 6
1, 3, 6, 30, 180, 1260, 10080, 90720, 907200, 9979200, 119750400, 1556755200, 21794572800, 326918592000, 5230697472000, 88921857024000, 1600593426432000, 30411275102208000, 608225502044160000, 12772735542927360000, 281000181944401920000 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
a(n-1), n>=5, gives the number of necklaces with n beads (C_n symmetry) with color signature determined from the partition 2^2,1^(n-4) of n. Only n-2 distinct colors, say c[1], c[2], ..., c[n-2] are used, and the representative necklaces have the color c[1] and c[2] each twice. E.g., n=5, partition 2,2,1, color signature (take the parts as exponents) c[1]c[1]c[2]c[2]c[3], with the a(4)=6 necklaces (write j for color c[j]) 11223, 11232, 11322, 12213, 12123 and 12132, all taken cyclically. See A212359 for the numbers for general partitions or color signatures. - Wolfdieter Lang, Jun 27 2012
LINKS
FORMULA
a(n) = numerator(n!/(2*(n! - 2))) for n > 2. - Stefano Spezia, Dec 06 2023
MATHEMATICA
f[n_]:=If[IntegerPart[n]==n, n, Numerator[n]]; a=1; lst={}; Do[a=n*a-a; AppendTo[lst, f[a/4]], {n, 3, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 28 2009 *)
Join[{1, 3}, Range[4, 30]!/4] (* Harvey P. Dale, Aug 13 2013 *)
PROG
(PARI) concat([1, 3], vector(66, n, (n+3)!/4)) \\ Joerg Arndt, Aug 14 2013
CROSSREFS
A diagonal of triangle A133800.
Cf. A212359.
Sequence in context: A265376 A318431 A157534 * A347925 A262022 A088436
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 17 2008
EXTENSIONS
Corrected parameters in definition. - Geoffrey Critzer, Apr 26 2009
STATUS
approved

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Last modified April 15 20:38 EDT 2024. Contains 371696 sequences. (Running on oeis4.)