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A071007 Number of permutations in the symmetric group S_n such that the maximal cycle has length exactly 3. 2
0, 0, 0, 2, 8, 40, 200, 980, 5152, 28448, 162080, 979000, 6179360, 40575392, 279199648, 1997406320, 14825619200, 114365751040, 912510870272, 7521873125408, 64045101880960, 561615674345600, 5067769601121920, 47023128008540992, 447820056115824128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

E.g.f.: exp( x + (x^2)/2 + (x^3)/3 ) - exp( x + (x^2)/2 ).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

FORMULA

a(n) = A057693(n) - A000085(n).

MATHEMATICA

nn=20; Range[0, nn]!CoefficientList[Series[Exp[x+x^2/2+x^3/3]-Exp[x+x^2/2], {x, 0, nn}], x]  (* Geoffrey Critzer, Jan 23 2013 *)

PROG

(PARI) for(n=0, 25, print1(polcoeff(serlaplace(exp(x+x^2/2+x^3/3)-exp(x+x^2/2)), n)", "))

CROSSREFS

Cf. A057693, A000085, A027617.

Column k=3 of A126074.

Sequence in context: A231125 A221587 A186947 * A027617 A187071 A154626

Adjacent sequences:  A071004 A071005 A071006 * A071008 A071009 A071010

KEYWORD

nonn

AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), May 19 2002

EXTENSIONS

More terms from Ralf Stephan, Apr 09 2003

STATUS

approved

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Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)