1,2

Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same structure.

Density of regular language L over {1,2,3,4,5,6}^* (i.e. number of strings of length n in L) described by regular expression with c=6: sum_{i=1..c}(prod_{j=1..i}(j(1+..+j)*) where sum stands for union and prod for concatenation. - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004

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.

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.

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.

Nelma Moreira and Rogerio Reis, dcc-2004-07.ps

sum from k=1 to k=6 of stirling2(n, k).

(1/6!)*(6^n+15*4^n+40*3^n+135*2^n+264). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 17 2003

For c=6, 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 - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004

Cf. A000351, A000400, A007581, A056272.

Cf. A008290.

Cf. A007051, A007581, A056272, A099263, A099262.

Sequence in context: A007296 A056272 A108304 this_sequence A099262 A108305 A099263

Adjacent sequences: A056270 A056271 A056272 this_sequence A056274 A056275 A056276

nonn

Marks R. Nester (nesterm(AT)dpi.qld.gov.au)