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Search: id:A099262
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| A099262 |
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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)). |
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+0
3
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| 1, 2, 5, 15, 52, 203, 877, 4139, 21110, 115179, 665479, 4030523, 25343488, 164029595, 1084948961, 7291973067, 49582466986, 339971207051, 2345048898523, 16244652278171
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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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.
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LINKS
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N. Moreira and R. Reisdcc-2004-07.ps
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FORMULA
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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
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CROSSREFS
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Cf. A007051, A007581, A056272, A056273, A099263.
Sequence in context: A056272 A108304 A056273 this_sequence A108305 A099263 A000110
Adjacent sequences: A099259 A099260 A099261 this_sequence A099263 A099264 A099265
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KEYWORD
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easy,nonn
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AUTHOR
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Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004
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