%I A099262
%S A099262 1,2,5,15,52,203,877,4139,21110,115179,665479,4030523,25343488,
%T A099262 164029595,1084948961,7291973067,49582466986,339971207051,2345048898523,
%U A099262 16244652278171
%N A099262 a(n) := 1/5040 7^n + 1/240 5^n + 1/72 4^n + 1/16 3^n + 11/60 2^n + 53/
               144 Partial sum of Stirling numbers of second kind S(n,i), i=1..7 
               (i.e. a(n)=sum_{i=1..7}S(n,i)).
%C A099262 Density of regular language L over {1,2,3,4,5,6,7} (i.e. number of strings 
               of length n in L) described by regular expression with c=7: sum_{i=1..c}(prod_{j=1..i}(j(1+..+j)*) 
               where sum stands for union and prod for concatenation.
%D A099262 Nelma Moreira and Rogerio Reis, On the density of languages representing 
               finite set partitions, Technical Report DCC-2004-07, August 2004, 
               DCC-FC& LIACC, Universidade do Porto.
%D A099262 N. Moreira and R. Reis, On the Density of Languages Representing Finite 
               Set Partitions, Journal of Integer Sequences, Vol. 8 (2005), Article 
               05.2.8.
%H A099262 N. Moreira and R. Reis, <a href="http://www.dcc.fc.up.pt/Pubs/TR04/dcc-2004-07.ps.gz">
               dcc-2004-07.ps</a>
%F A099262 For c=7, a(n)= (c^n)/c!+sum_{k=1..c-2}((k^n)/k!*(sum_{j=2..c-k}(((-1)^j)/
               j!))) or = sum_{k=1..c}(g(k, c)*k^n) where g(1, 1)=1 g(1, c)=g(1, 
               c-1)+((-1)^(c-1))/(c-1)!, c>1 g(k, c)=g(k-1, c-1)/k, for c>1 and 
               2<= k<= c
%Y A099262 Cf. A007051, A007581, A056272, A056273, A099263.
%Y A099262 Sequence in context: A056273 A141080 A148092 this_sequence A141081 A108305 
               A099263
%Y A099262 Adjacent sequences: A099259 A099260 A099261 this_sequence A099263 A099264 
               A099265
%K A099262 easy,nonn
%O A099262 1,2
%A A099262 Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004