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Search: id:A099263
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| A099263 |
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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)). |
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+0
3
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| 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115929, 677359, 4189550, 27243100, 184941915, 1301576801, 9433737120, 69998462014, 529007272061, 4054799902003, 31415584940850, 245382167055488, 1928337630016767, 15222915798289765
(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 {1,2,3,4,5,6,7,8} (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.
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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=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
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CROSSREFS
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Cf. A007051, A007581, A056272, A056273, A099262.
Sequence in context: A056273 A099262 A108305 this_sequence A000110 A134381 A107589
Adjacent sequences: A099260 A099261 A099262 this_sequence A099264 A099265 A099266
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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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