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A002874 The number of partitions of {1..3n} that are invariant under a permutation consisting of n 3-cycles.
(Formerly M1863 N0738)
15
1, 2, 8, 42, 268, 1994, 16852, 158778, 1644732, 18532810, 225256740, 2933174842, 40687193548, 598352302474, 9290859275060, 151779798262202, 2600663778494172, 46609915810749130, 871645673599372868, 16971639450858467002, 343382806080459389676 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Original name: Sorting numbers.

Equals column 3 of A162663. - Michel Marcus, Mar 27 2013

REFERENCES

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).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..484 (first 101 terms from T. D. Noe)

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

FORMULA

E.g.f.: exp( (exp(3*x) - 4)/3 + exp(x) ).

MAPLE

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

# second Maple program:

a:= proc(n) option remember; `if`(n=0, 1, add((1+

      3^(j-1))*binomial(n-1, j-1)*a(n-j), j=1..n))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Oct 17 2017

MATHEMATICA

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 *)

CROSSREFS

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

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

New name from Danny Rorabaugh, Oct 24 2015

STATUS

approved

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Last modified June 21 21:23 EDT 2018. Contains 305642 sequences. (Running on oeis4.)