4,2

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

T. D. Noe, Table of n, a(n) for n=4..200

Eric Weisstein's World of Mathematics, Eulerian Number

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

There is one permutation of 4 with exactly 3 descents (4321) and there are 26 permutations of 5 with 3 descents.

A000498:=proc(n); 4^n-(n+1)*3^n+1/2*(n)*(n+1)*2^n-1/6*(n-1)*(n)*(n+1); end:

Cf. A066912.

Sequence in context: A010831 A022718 A014472 this_sequence A066912 A015800 A030647

Adjacent sequences: A000495 A000496 A000497 this_sequence A000499 A000500 A000501

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)

More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000