%I A052186
%S A052186 1,0,1,3,14,77,497,3676,30677,285335,2928846,32903721,401739797,
%T A052186 5298600772,75092880273,1138261010851,18378421938366,314928827507717,
%U A052186 5708689036074089,109145365739197964,2195167574579322013
%N A052186 Number of permutations of [n] with no strong fixed points.
%C A052186 Equals INVERTi transform of the factorials, n starting with 0. Triangle 
               A144108 has row sums = n! with left border = A052186. [From Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008]
%D A052186 Stanley, R., Enumerative Combinatorics, Volume 1 (1986), p. 49
%H A052186 J. W. Layman, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               The Hankel Transform and Some of its Properties</a>, J. Integer Sequences, 
               4 (2001), #01.1.5.
%H A052186 V. Strehl, <a href="a003149.pdf">The average number of splitters in a 
               random permutation</a> [Unpublished; included here with the author's 
               permission.]
%F A052186 G.f.: F(x)/(1+x*F(x)), F(x) = Sum_{n >= 0} n!*x^n.
%F A052186 a(0)=1, a(1)=0, a(n) = (n-2)*a(n-1) + Sum_{k=0..n-1} a(k)*a(n-1-k) + 
               Sum_{k=0..k-2} a(k)*a(n-2-k) if n>1. - Michael Somos Oct 11 2006
%p A052186 t1 := sum(n!*x^n, n=0..100): F := series(t1/(1+x*t1), x, 100): for i 
               from 0 to 20 do printf(`%d, `, coeff(F, x, i)) od:# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 22 2009]
%o A052186 (PARI) {a(n)=if(n<0, 0, polcoeff( 1/ (x+1/sum(k=0, n, k!*x^k, x*O(x^n))), 
               n))} /* Michael Somos Oct 11 2006 */
%Y A052186 Cf. A006932.
%Y A052186 Cf. A144108, A000142 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 
               11 2008]
%Y A052186 Sequence in context: A133798 A100937 A048779 this_sequence A074538 A001564 
               A059276
%Y A052186 Adjacent sequences: A052183 A052184 A052185 this_sequence A052187 A052188 
               A052189
%K A052186 nonn,easy,nice
%O A052186 0,4
%A A052186 N. J. A. Sloane (njas(AT)research.att.com), Feb 04 2000
%E A052186 Better description from James A. Sellers (sellersj(AT)math.psu.edu), 
               Mar 13 2000