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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 J. Pasukonis, S. Ramgoolam, From counting to construction for BPS states in N=4SYM, J. High En. Phys. 2011 (2) (2011) # 078 arXiv:1010.1683 doi:10.1007/JHEP02(2011)078, (E.3) 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) 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 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 EXTENSIONS New name from Danny Rorabaugh, Oct 24 2015 STATUS approved

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Last modified August 17 23:07 EDT 2018. Contains 313817 sequences. (Running on oeis4.)