Search: id:A000498
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%I A000498 M5188 N2255
%S A000498 1,26,302,2416,15619,88234,455192,2203488,10187685,45533450,198410786,
%T A000498 848090912,3572085255,14875399450,61403313100,251732291184,
%U A000498 1026509354985,4168403181210,16871482830550,68111623139600
%N A000498 Eulerian numbers. Column 4 of Euler's triangle A008292. Number of permutations 
               of n letters with exactly 3 descents.
%D A000498 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000498 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000498 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%D A000498 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.
%D A000498 F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, 
               p. 151.
%D A000498 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 260.
%D A000498 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               215.
%H A000498 T. D. Noe, <a href="b000498.txt">Table of n, a(n) for n=4..200</a>
%H A000498 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EulerianNumber.html">Eulerian Number</a>
%F A000498 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
%e A000498 There is one permutation of 4 with exactly 3 descents (4321) and there 
               are 26 permutations of 5 with 3 descents.
%p A000498 A000498:=proc(n); 4^n-(n+1)*3^n+1/2*(n)*(n+1)*2^n-1/6*(n-1)*(n)*(n+1); 
               end:
%Y A000498 Cf. A066912.
%Y A000498 Sequence in context: A010831 A022718 A014472 this_sequence A066912 A015800 
               A030647
%Y A000498 Adjacent sequences: A000495 A000496 A000497 this_sequence A000499 A000500 
               A000501
%K A000498 nonn,nice
%O A000498 4,2
%A A000498 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. 
               Wilson v (rgwv(AT)rgwv.com)
%E A000498 More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000

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