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A001785
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Second order reciprocal Stirling number (Fekete) [[2n+4, n]]. The number of n-orbit permutations of a (2n+4)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet).
(Formerly M5382 N2338)
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3
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1, 120, 7308, 303660, 11098780, 389449060, 13642629000, 486591585480, 17856935296200, 678103775949600, 26726282654771700, 1094862336960892500, 46641683693715610500, 2066075391660447667500, 95122549872697437090000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| [[2n+4, n]]=sum((-1)^i*binomial(2n+4, 2n+4-i)[2n+4-i, n-i] where [n, k] is the unsigned Stirling number of the first kind.
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MAPLE
| 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+4, j); od;
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CROSSREFS
| Cf. A000907, A000483, A001784.
Sequence in context: A055213 A035190 A035815 * A156411 A076005 A104592
Adjacent sequences: A001782 A001783 A001784 * A001786 A001787 A001788
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms, Maple program, formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
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