3,2

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

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.

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.

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.

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; [Conjectured by 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.

Adjacent sequences: A000457 A000458 A000459 this_sequence A000461 A000462 A000463

Sequence in context: A008493 A001287 A022576 this_sequence A030115 A091929 A058883

nonn

njas, 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