A071007 Number of permutations in the symmetric group S_n such that the maximal cycle has length exactly 3.

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

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