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A099266
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a(6,n) := 1/600 6^n + 1/36 4^n + 1/12 3^n + 3/8 2^n + 11/30 n - 439/900 Partial sum of A056273(= sum_{m=1..n}sum_{i=1..6}S(m,i)) (i.e. partial sum of Stirling numbers of second kind S(n,i) for i=1..6)).
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1
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1, 3, 8, 23, 75, 278, 1154, 5265, 25913, 135212, 736704, 4139831, 23767895, 138468210, 814675838, 4824766301, 28699128501, 171207852152, 1023332115836, 6124430348355, 36684624841811, 219860794899518, 1318179574171578
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Density of regular language L{0}* over {0,1,2,3,4,5,6} (i.e. number of strings of length n), where L is 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. I.e L=L((11*+...+11*2(1+2)*3(1+2+3)*4(1+2+3+4)*5(1+2+3+4+5)*6(1+2+3+4+5+6)*)0*)
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REFERENCES
| 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
| dcc-2004-07.ps
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FORMULA
| For c=6, a(c, n)=g(1, c)*n+sum_{k=2..c}((g(k, c)*k*(k^n - 1))/(k - 1)) 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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MAPLE
| with (combinat):seq(sum(sum(stirling2(k, j), j=1..6), k=1..n), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 04 2007
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CROSSREFS
| Cf. A056273, A047926, A099264, A099265.
Sequence in context: A151405 A148778 A099265 * A024716 A189359 A125782
Adjacent sequences: A099263 A099264 A099265 * A099267 A099268 A099269
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KEYWORD
| easy,nonn
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AUTHOR
| Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004
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