OFFSET
1,5
REFERENCES
D. M. Jackson, J. W. Reilly, Permutations with a prescribed number of $p$-runs. Ars Combinatoria 1 (1976), no. 1, 297-305.
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
J. Riordan, Permutations without 3-sequences, Bull. Amer. Math. Soc., 51 (1945), 745-748.
MATHEMATICA
nmax = 22;
CoefficientList[Sum[((m + 2)*(m + 1)*(m + 2)!/2*(x^6*(1 - x)^4/(1 - x^3)^4) + (m + 1)*(m + 1)!*(x^4*(1 + x)*(1 - x)^3)/(1 - x^3)^3)*((x - x^3)/(1 - x^3))^m, {m, 0, nmax}]/x + O[x]^nmax, x] (* Jean-François Alcover, May 06 2024, after Tani Akinari *)
PROG
(PARI) concat([0, 0, 0], Vec(sum(m=0, 100, ((m+2)*(m+1)*(m+2)!/2*(x^6*(1-x)^4/(1-x^3)^4)+(m+1)*(m+1)!*(x^4*(1+x)*(1-x)^3)/(1-x^3)^3)*((x-x^3)/(1-x^3))^m)+O(x^100))) \\ Tani Akinari, Nov 08 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Max Alekseyev, Feb 20 2010
STATUS
approved