%I A099263
%S A099263 1,2,5,15,52,203,877,4140,21146,115929,677359,4189550,27243100,
%T A099263 184941915,1301576801,9433737120,69998462014,529007272061,4054799902003,
%U A099263 31415584940850,245382167055488,1928337630016767,15222915798289765
%N A099263 a(n) = 1/40320 8^n + 1/1440 6^n + 1/360 5^n + 1/64 4^n + 11/180 3^n + 
               53/288 2^n + 103/280 Partial sum of Stirling numbers of second kind 
               S(n,i), i=1..8 (i.e. a(n)=sum_{i=1..8}S(n,i)).
%C A099263 Density of regular language L over {1,2,3,4,5,6,7,8} (i.e. number of 
               strings of length n in L) described by regular expression with c=8: 
               sum_{i=1..c}(prod_{j=1..i}(j(1+..+j)*) where sum stands for union 
               and prod for concatenation.
%D A099263 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 A099263 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 A099263 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 A099263 For c=8, 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 A099263 Cf. A007051, A007581, A056272, A056273, A099262.
%Y A099263 Sequence in context: A099262 A141081 A108305 this_sequence A164863 A164864 
               A000110
%Y A099263 Adjacent sequences: A099260 A099261 A099262 this_sequence A099264 A099265 
               A099266
%K A099263 easy,nonn
%O A099263 1,2
%A A099263 Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004