A220860 - OEIS

%I #11 Jul 24 2014 06:41:11

%S 1,1,1,1,4,1,1,10,9,1,20,41,6,1,35,133,61,2,1,56,350,336,49,1,84,798,

%T 1336,465,20,1,120,1638,4300,2789,380,4,1,165,3102,11902,12577,3581,

%U 192,1,220,5511,29392,46487,22924,3025,56

%N Triangle read by rows related to enumeration of permutations avoiding certain patterns.

%C See Barnabei et al. (2012) for precise definition.

%H M. Barnabei, F. Bonetti and M. Silimbani, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i3p25">Two permutation classes related to the Bubble Sort operator</a>, Electronic Journal of Combinatorics 19(3) (2012), #P25. See Theorem 6.

%e Triangle begins:

%e 1

%e 1 1

%e 1 4   1

%e 1 10  9

%e 1 20  41   6

%e 1 35  133  61   2

%e 1 56  350  336  49

%e 1 84  798  1336 465  20

%e 1 120 1638 4300 2789 380 4

%e ...

%o (PARI) rows(nn) = {my(pol = Pol((1 - 3*x + 3*x^2 - 3*x^2*y - x^3 + 2*x^3*y - x^3*y^2)/(1 - 4*x + 6*x^2 - 4*x^2*y - 4*x^3 + 6*x^3*y - 2*x^3*y^2 + x^4 - 2*x^4*y + x^4*y^2) + O(x^nn))); for (i=1, poldegree(pol, x), ypol = polcoeff(pol, i, x); for (j=0, poldegree(ypol, y), print1(polcoeff(ypol, j, y), ", ");); print(););} \\ _Michel Marcus_, Jul 23 2014

%Y Cf. A000292 (second column).

%K nonn,tabf

%O 1,5

%A _N. J. A. Sloane_, Dec 25 2012

%E More terms from _Michel Marcus_, Jul 23 2014

%E Keyword set to tabf by _Michel Marcus_, Jul 23 2014