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Search: id:A001784
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| A001784 |
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Second order reciprocal Stirling number (Fekete) [[2n+3 \over n]]. The number of n-orbit permutations of a (2n+3)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet).
(Formerly M5169 N2244)
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+0
4
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| 1, 24, 924, 26432, 705320, 18858840, 520059540, 14980405440, 453247114320, 14433720701400, 483908513388300, 17068210823664000, 632607429473019000, 24602295329058447000, 1002393959071727722500, 42720592574082543120000
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.
C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 152.
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FORMULA
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[[2n+3, n]]=sum((-1)^i*binomial(2n+3, 2n+3-i)[2n+3-i, n-i] where [n, k] is the unsigned Stirling number of the first kind.
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MAPLE
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with(combinat):s1 := (n, k)->sum((-1)^i*binomial(n, i)*abs(stirling1(n-i, k-i)), i=0..n); for j from 1 to 20 do s1(2*j+3, j); od;
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CROSSREFS
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Cf. A000907, A000483, A001785.
Sequence in context: A107391 A006147 A061236 this_sequence A001866 A033590 A006175
Adjacent sequences: A001781 A001782 A001783 this_sequence A001785 A001786 A001787
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms, Maple program, formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
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