%I A097900
%S A097900 1,2,7,32,180,1200,9240,80640,786240,8467200,99792000,1277337600,
%T A097900 17643225600,261534873600,4140968832000,69742632960000,1244905998336000,
%U A097900 23475370254336000,466306218233856000,9731608032706560000
%N A097900 Number of runs of length 1 in all permutations of [n]. (The permutation 
               3574162 has two runs of length 1: 357/4/16/2).
%D A097900 Ira. M. Gessel, Generating functions and enumeration of sequences, Ph. 
               D. Thesis, MIT, 1977.
%F A097900 a(n)=n!(n+4)/6 for n>=2. E.g.f.= x(6-6x+x^2)/[6(1-x)^2].
%e A097900 a(3)=7 because there are 7 runs of length 1 in the permutations 123, 
               13(2),
%e A097900 (2)13, 23(1), (3)12, (3)(2)(1) (shown between parentheses).
%p A097900 1,seq(n!*(n+4)/6,n=2..23);
%Y A097900 Sequence in context: A059439 A006014 A121555 this_sequence A000153 A006154 
               A000987
%Y A097900 Adjacent sequences: A097897 A097898 A097899 this_sequence A097901 A097902 
               A097903
%K A097900 nonn
%O A097900 1,2
%A A097900 Emeric Deutsch (deutsch(AT)duke.poly.edu) and Ira Gessel (gessel(AT)brandeis.edu), 
               Sep 03 2004