Search: id:A000460
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%I A000460 M4795 N2047
%S A000460 1,11,66,302,1191,4293,14608,47840,152637,478271,1479726,4537314,
%T A000460 13824739,41932745,126781020,382439924,1151775897,3464764515,
%U A000460 10414216090,31284590870,93941852511,282010106381,846416194536
%N A000460 Eulerian numbers. (Column 3 of Euler's triangle A008292.)
%C A000460 Number of permutations of [n] with exactly 2 descents. - Mike Zabrocki 
               (zabrocki(AT)mathstat.yorku.ca), Nov 10 2004
%D A000460 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%D A000460 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.
%D A000460 F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, 
               p. 151.
%D A000460 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 260.
%D A000460 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               215.
%D A000460 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000460 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000460 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A000460 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A000460 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EulerianNumber.html">Eulerian Number</a>
%F A000460 3^(n+2) - (n+3)*2^(n+2) + (1/2)*(n+2)*(n+3) - Randall L. Rathbun (randallr(AT)abac.com), 
               Jan 22 2002
%F A000460 G.f.: x^3*(1+x-4*x^2)/((1-x)^3*(1-2*x)^2*(1-3*x)). - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), 
               Nov 10 2004
%p A000460 A000460:=-z*(-1-z+4*z**2)/(-1+3*z)/(2*z-1)**2/(z-1)**3; [S. Plouffe in 
               his 1992 dissertation.]
%o A000460 (PARI) A000460(n) = 3^(n+2)-(n+3)*2^(n+2)+(1/2)*(n+2)*(n+3)
%Y A000460 Cf. A008292.
%Y A000460 Cf. A000295.
%Y A000460 Sequence in context: A008493 A001287 A022576 this_sequence A030115 A091929 
               A058883
%Y A000460 Adjacent sequences: A000457 A000458 A000459 this_sequence A000461 A000462 
               A000463
%K A000460 nonn
%O A000460 3,2
%A A000460 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. 
               Wilson v (rgwv(AT)rgwv.com)
%E A000460 More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000
%E A000460 More terms from Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 10 
               2004

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