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A000544
Number of permutations of length n by rises.
(Formerly M3110 N1260)
1
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).
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
KEYWORD
nonn
EXTENSIONS
More terms from Vladeta Jovovic, Nov 23 2007
Generating function from Sean A. Irvine, Nov 18 2010
STATUS
approved