3,2

Number of permutations of [n] with exactly 2 descents. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 10 2004

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.

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).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Eric Weisstein's World of Mathematics, Eulerian Number

3^(n+2) - (n+3)*2^(n+2) + (1/2)*(n+2)*(n+3) - Randall L. Rathbun (randallr(AT)abac.com), Jan 22 2002

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

A000460:=-z*(-1-z+4*z**2)/(-1+3*z)/(2*z-1)**2/(z-1)**3; [S. Plouffe in his 1992 dissertation.]

(PARI) A000460(n) = 3^(n+2)-(n+3)*2^(n+2)+(1/2)*(n+2)*(n+3)

Cf. A008292.

Cf. A000295.

Sequence in context: A008493 A001287 A022576 this_sequence A030115 A091929 A058883

Adjacent sequences: A000457 A000458 A000459 this_sequence A000461 A000462 A000463

nonn

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

More terms from Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 10 2004