A082680 - OEIS

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A082680

Triangle read by rows: 2-stack sortable n-permutations with k runs.

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; internal format)

	OFFSET	`1,5`
	COMMENTS	`beta(1,0)-trees on n+1 nodes with k leaves.`
	LINKS	`M. Bona, [math/9705220] 2-stack sortable permutations with a given number of runs`
	FORMULA	`T(k, n) = (n+k-1)!(2n-k)!/k!/(n+1-k)!/(2k-1)!/(2n-2*k+1)!.`
	CROSSREFS	`Cf. T(k, 2) = A000292(k). T(k, 3) = A051947(k).` `Sequence in context: A174043 A175124 A089447 * A056939 A202924 A142595` `Adjacent sequences: A082677 A082678 A082679 * A082681 A082682 A082683`
	KEYWORD	`nonn,tabl,easy`
	AUTHOR	`Ralf Stephan (ralf(AT)ark.in-berlin.de), May 19 2003`

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Last modified February 14 16:21 EST 2012. Contains 205635 sequences.