A055303 - OEIS

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A055303

Number of labeled rooted trees with n nodes and 2 leaves.

3, 36, 360, 3600, 37800, 423360, 5080320, 65318400, 898128000, 13172544000, 205491686400, 3399953356800, 59499183744000, 1098446469120000, 21341245685760000, 435361411989504000, 9305850181275648000 (list; graph; refs; listen; history; internal format)

	OFFSET	`3,1`
	COMMENTS	`a(n+1) is the sum of the zero moments over all permutations of n. E.g. a(4) is [1,2,3].[0,1,2] + [1,3,2].[0,1,2] + [2,1,3].[0,1,2] + [2,3,1].[0,1,2] + [3,1,2].[0,1,2] + [3,2,1].[0,1,2] = 8 + 7 + 7 + 5 + 5 + 4 = 36. - Jon Perry (perry(AT)globalnet.co.uk), Feb 20 2004`
	LINKS	`Index entries for sequences related to rooted trees`
	FORMULA	`E.g.f.: x^3/(2(1-x)^3).` `a(n)=(n-2)!t(n-2)t(n-1) = (n-2)!(n-2)(n-1)^2n/4 = n!(n-2)(n-1)/4 = n!*t(n-2)/2 - Jon Perry (perry(AT)globalnet.co.uk), Feb 22 2004`
	MAPLE	`seq((n-1)!(n-2)(n-3)*(n-4)/144, n = 5..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2008`
	CROSSREFS	`Column 2 of A055302.` `Sequence in context: A067444 A092648 A026121 * A068177 A099670 A199258` `Adjacent sequences: A055300 A055301 A055302 * A055304 A055305 A055306`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), May 11 2000`

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Last modified February 15 19:15 EST 2012. Contains 205852 sequences.