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}^* (i.e. number of strings of length n in L) described by regular expression 11*+11*2(1+2)*+11*2(1+2)*3(1+2+3)*+ 11*2(1+2)*3(1+2+3)*4(1+2+3+4)*+11*2(1+2)*3(1+2+3)*4(1+2+3+4)*5(1+2+3+4+5)* - 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=5 of stirling2(n, k).

(1/5!)*(5^n+10*3^n+20*2^n+45). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 17 2003

For c=5, 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

with (combinat):seq(sum(stirling2(n, j), j=1..5), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 04 2007

Cf. A000351, A007581, A056273.

Cf. A008290.

Cf. A007051, A007581, A056273.

Sequence in context: A053553 A007312 A007296 this_sequence A140980 A108304 A158829

Adjacent sequences: A056269 A056270 A056271 this_sequence A056273 A056274 A056275

nonn

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