A000544 - OEIS

%I M3110 N1260 #23 Feb 04 2022 02:01:40

%S 3,25,155,1005,7488,64164,619986,6646750,78161249,999473835,

%T 13801761213,204631472475,3241541125110,54629642149630,

%U 975867376041308,18416844056075364,366128842105397631,7647337600268371485,167424323805645018159,3833790834030516355705,91641405910147125954428,2282611988081527293910920

%N Number of permutations of length n by rises.

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

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

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

%F 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).

%t 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 *)

%Y Cf. A010030.

%K nonn

%O 4,1

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Nov 23 2007

%E Generating function from _Sean A. Irvine_, Nov 18 2010