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A002874
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The number of partitions of {1..3n} that are invariant under a permutation consisting of n 3-cycles.
(Formerly M1863 N0738)
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13
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1, 2, 8, 42, 268, 1994, 16852, 158778, 1644732, 18532810, 225256740, 2933174842, 40687193548, 598352302474, 9290859275060, 151779798262202, 2600663778494172, 46609915810749130, 871645673599372868
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OFFSET
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0,2
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COMMENTS
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Original name: Sorting numbers.
Equals column 3 of A162663. - Michel Marcus, Mar 27 2013
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
OEIS Wiki, Sorting numbers
Index entries for sequences related to sorting
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FORMULA
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E.g.f.: exp( (exp(3*x) - 4)/3 + exp(x) ).
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MAPLE
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S:= series(exp( (exp(3*x) - 4)/3 + exp(x)), x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, Oct 30 2015
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MATHEMATICA
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u[0, j_]:=1; u[k_, j_]:=u[k, j]=Sum[Binomial[k-1, i-1]Plus@@(u[k-i, j]#^(i-1)&/@Divisors[j]), {i, k}]; Table[u[n, 3], {n, 0, 12}] (* Wouter Meeussen, Dec 06 2008 *)
mx = 16; p = 3; Range[0, mx]! CoefficientList[ Series[ Exp[ (Exp[p*x] - p - 1)/p + Exp[x]], {x, 0, mx}], x] (* Robert G. Wilson v, Dec 12 2012 *)
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CROSSREFS
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u[n,j] generates for j=1, A000110; j=2, A002872; j=3, this sequence; j=4, A141003; j=5, A036075; j=6, A141004; j=7, A036077. - Wouter Meeussen, Dec 06 2008
Sequence in context: A005315 A182520 A121635 * A078592 A225108 A052646
Adjacent sequences: A002871 A002872 A002873 * A002875 A002876 A002877
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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EXTENSIONS
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New name from Danny Rorabaugh, Oct 24 2015
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STATUS
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approved
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