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A082680 Triangle read by rows: 2-stack sortable n-permutations with k runs. 3
1, 1, 1, 1, 4, 1, 1, 10, 10, 1, 1, 20, 49, 20, 1, 1, 35, 168, 168, 35, 1, 1, 56, 462, 900, 462, 56, 1, 1, 84, 1092, 3630, 3630, 1092, 84, 1, 1, 120, 2310, 12012, 20449, 12012, 2310, 120, 1, 1, 165, 4488, 34320, 91091, 91091 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

beta(1,0)-trees on n+1 nodes with k leaves.

Row sums are given by A000139. - F. Chapoton, Nov 17 2015

LINKS

Table of n, a(n) for n=1..51.

M. Bona, 2-stack sortable permutations with a given number of runs, arXiv:math/9705220 [math.CO], 1997.

Enrica Duchi, Veronica Guerrini, Simone Rinaldi, Gilles Schaeffer, Fighting Fish: enumerative properties, arXiv:1611.04625 [math.CO], 2016.

FORMULA

T(k, n) = (n+k-1)!*(2*n-k)!/k!/(n+1-k)!/(2*k-1)!/(2*n-2*k+1)!.

EXAMPLE

Triangle starts:

1;

1,  1;

1,  4,    1;

1, 10,   10,    1;

1, 20,   49,   20,    1;

1, 35,  168,  168,   35,    1;

1, 56,  462,  900,  462,   56,  1;

1, 84, 1092, 3630, 3630, 1092, 84, 1;

...

CROSSREFS

Cf. A000292 (2nd column), A051947(3rd column).

Cf. A000139 (row sums).

Sequence in context: A319029 A175124 A089447 * A056939 A202924 A142595

Adjacent sequences:  A082677 A082678 A082679 * A082681 A082682 A082683

KEYWORD

nonn,tabl,easy

AUTHOR

Ralf Stephan, May 19 2003

STATUS

approved

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Last modified April 19 02:52 EDT 2019. Contains 322237 sequences. (Running on oeis4.)