A000544 Number of permutations of length n by rises. (Formerly M3110 N1260)

3, 25, 155, 1005, 7488, 64164, 619986, 6646750, 78161249, 999473835, 13801761213, 204631472475, 3241541125110, 54629642149630, 975867376041308, 18416844056075364, 366128842105397631, 7647337600268371485, 167424323805645018159, 3833790834030516355705, 91641405910147125954428, 2282611988081527293910920

Offset

4,1

References

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264.

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).

Links

Table of n, a(n) for n=4..25.

Formula

G.f.: x^2*Sum_{k>=0} k*k!*(x^2-x+k-1)*(-x*(x-1)/(x+1))^k/((x^2-1)^2*(x-1)^2).

Mathematica

max = 22; s = Sum[k*k!*(x^2-x+k-1)*(-x*(x-1)/(x+1))^k, {k, 1, max+1}]/(x- x^2-x^3+x^4)^2 + O[x]^max; CoefficientList[s, x] (* Jean-François Alcover, Feb 09 2016 *)

Crossrefs

Cf. A010030.

Sequence in context: A277520 A367507 A303602 * A356200 A221777 A227995

Adjacent sequences: A000541 A000542 A000543 * A000545 A000546 A000547

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Nov 23 2007

Generating function from Sean A. Irvine, Nov 18 2010

Status

approved