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A220860
Triangle read by rows related to enumeration of permutations avoiding certain patterns.
0
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, 1336, 465, 20, 1, 120, 1638, 4300, 2789, 380, 4, 1, 165, 3102, 11902, 12577, 3581, 192, 1, 220, 5511, 29392, 46487, 22924, 3025, 56
OFFSET
1,5
COMMENTS
See Barnabei et al. (2012) for precise definition.
LINKS
M. Barnabei, F. Bonetti and M. Silimbani, Two permutation classes related to the Bubble Sort operator, Electronic Journal of Combinatorics 19(3) (2012), #P25. See Theorem 6.
EXAMPLE
Triangle begins:
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 1336 465 20
1 120 1638 4300 2789 380 4
...
PROG
(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
CROSSREFS
Cf. A000292 (second column).
Sequence in context: A361731 A109955 A214398 * A174043 A319029 A175124
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Dec 25 2012
EXTENSIONS
More terms from Michel Marcus, Jul 23 2014
Keyword set to tabf by Michel Marcus, Jul 23 2014
STATUS
approved