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A069321
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Stirling transform of A001563 : a(0)=1, a(n)=sum(stirling2(n,k)*k*k!,k=1..n), n=1,2...
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7
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1, 1, 5, 31, 233, 2071, 21305, 249271, 3270713, 47580151, 760192505, 13234467511, 249383390393, 5057242311031, 109820924003705, 2542685745501751, 62527556173577273, 1627581948113854711, 44708026328035782905
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The number of compatible bipartitions of a set of cardinality n for which at least one subset is not underlined. E.g. for n=2 there are 5 such bipartitions: {1 2}, {1}{2}, {2}{1}, _{1}_{2}, _{2}_{1}. A005649 is the number of bipartitions of a set of cardinality n. A000670 is the number of bipartitions of a set of cardinality n with none of the subsets underlined. - T. Kyle Petersen (tkpeters(AT)brandeis.edu), Mar 31 2005
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REFERENCES
| B. Cloitre, On the fractal behavior of primes, 2011; http://bcmathematics.monsite-orange.fr/FractalOrderOfPrimes.pdf
D. Foata and D. Zeilberger, "Graphical major indices," J. Comput. Appl. Math. 68 (1996), no. 1-2, 79-101.
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LINKS
| D. Foata and D. Zeilberger, The Graphical Major Index.
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FORMULA
| Representation as an infinite series, in Maple notation : a(0)=1, a(n)= sum(k^n*(k-1)/(2^k), k=2..infinity)/4, n=1, 2... This is a Dobinski-type summation formula. E.g.f.: (exp(x)-1)/((2-exp(x))^2).
a(n)=(A000629(n+1)-A000629(n))/4 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 20 2002
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CROSSREFS
| Cf. A001563.
a(n) = (1/2)*(A000670(n+1)-A000670(n)).
Cf. A005649, A000670.
Sequence in context: A001910 A052773 A062147 * A177797 A186859 A082579
Adjacent sequences: A069318 A069319 A069320 * A069322 A069323 A069324
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Mar 14 2002
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