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Search: id:A000498
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| A000498 |
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Eulerian numbers. Column 4 of Euler's triangle A008292. Number of permutations of n letters with exactly 3 descents.
(Formerly M5188 N2255)
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+0
3
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| 1, 26, 302, 2416, 15619, 88234, 455192, 2203488, 10187685, 45533450, 198410786, 848090912, 3572085255, 14875399450, 61403313100, 251732291184, 1026509354985, 4168403181210, 16871482830550, 68111623139600
(list; graph; listen)
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OFFSET
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4,2
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REFERENCES
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L. Carlitz et al., Permutations and sequences with repetions by number of increases, J. Combin. Theory, 1 (1966), 350-374.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.
F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, p. 151.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 215.
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LINKS
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T. D. Noe, Table of n, a(n) for n=4..200
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FORMULA
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G.f.: x^4*(1+6*x-43*x^2+44*x^3+52*x^4-72*x^5)/((1-x)^4*(1-2*x)^3*(1-3*x)^2*(1-4*x)); a(n) = 4^n-(n+1)*3^n+1/2*(n)*(n+1)*2^n-1/6*(n-1)*(n)*(n+1). - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 12 2004
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EXAMPLE
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There is one permutation of 4 with exactly 3 descents (4321) and there are 26 permutations of 5 with 3 descents.
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MAPLE
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A000498:=proc(n); 4^n-(n+1)*3^n+1/2*(n)*(n+1)*2^n-1/6*(n-1)*(n)*(n+1); end:
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CROSSREFS
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Cf. A066912.
Adjacent sequences: A000495 A000496 A000497 this_sequence A000499 A000500 A000501
Sequence in context: A010831 A022718 A014472 this_sequence A066912 A015800 A030647
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KEYWORD
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nonn,nice
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AUTHOR
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njas, Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000
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