%I A000138 M1635 N0638
%S A000138 1,1,2,6,18,90,540,3780,31500,283500,2835000,31185000,372972600,
%T A000138 4848643800,67881013200,1018215198000,16294848570000,277012425690000,
%U A000138 4986223662420000,94738249585980000,1894745192712372000
%N A000138 Expansion of exp (-x^4 /4) / (1-x).
%C A000138 a(n) is the number of permutations in the symmetric group S_n whose cycle 
               decomposition contains no 4-cycle.
%D A000138 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000138 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000138 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               85.
%D A000138 R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, page 
               93, problem 7.
%H A000138 T. D. Noe, <a href="b000138.txt">Table of n, a(n) for n=0..100</a>
%F A000138 a(n) = n! * sum i=0 ... [n/4]( (-1)^i /(i! * 4^i)); a(n)/n! ~ sum i >
               = 0 (-1)^i /(i! * 4^i) = e^(-1/4); a(n) ~ e^(-1/4) * n!; a(n) ~ e^(-1/
               4) * (n/e)^n * sqrt(2 * Pi * n). - Avi Peretz (njk(AT)netvision.net.il), 
               Apr 22 2001
%e A000138 a(4) = 18 because in S_4 the permutations with no 4-cycle are the complement 
               of the six 4-cycles so a(4) = 4! - 6 = 18.
%o A000138 (PARI) {a(n) = if( n<0, 0, n! * polcoeff( exp( -(x^4 / 4) + x*O(x^n)) 
               / (1 - x), n))} /* Michael Somos Jul 28 2009 */ - Entry improved 
               by comments from Michael Somos Jul 28 2009
%Y A000138 Cf. A000142, A000090.
%Y A000138 Sequence in context: A118455 A165774 A053505 this_sequence A028857 A052687 
               A162059
%Y A000138 Adjacent sequences: A000135 A000136 A000137 this_sequence A000139 A000140 
               A000141
%K A000138 nonn,easy
%O A000138 0,3
%A A000138 N. J. A. Sloane (njas(AT)research.att.com).
%E A000138 Entry improved by comments from Michael Somos Jul 28 2009