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Search: id:A000907
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| A000907 |
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Second order reciprocal Stirling number (Fekete) [[2n+2 \over n]]. The number of n-orbit permutations of a (2n+2)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet).
(Formerly M4298 N1797)
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+0
4
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| 6, 130, 2380, 44100, 866250, 18288270, 416215800, 10199989800, 268438920750, 7562120816250, 227266937597700, 7262844156067500, 246045975136211250, 8810836639999143750, 332624558868351750000, 13205706717164131170000
(list; graph; listen)
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OFFSET
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0,1
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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+2, n]]=sum((-1)^i*binomial(2n+2, 2n+2-i)[2n+2-i, n-i] where [n, k] is the unsigned Stirling number of the first kind.
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MAPLE
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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+2, j); od;
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CROSSREFS
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Cf. A000483, A001784, A001785.
Sequence in context: A012842 A012638 A095695 this_sequence A077031 A137038 A024276
Adjacent sequences: A000904 A000905 A000906 this_sequence A000908 A000909 A000910
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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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