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Search: id:A055303
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A055303 Number of labeled rooted trees with n nodes and 2 leaves. +0
3
3, 36, 360, 3600, 37800, 423360, 5080320, 65318400, 898128000, 13172544000, 205491686400, 3399953356800, 59499183744000, 1098446469120000, 21341245685760000, 435361411989504000, 9305850181275648000 (list; graph; listen)
OFFSET

3,1

COMMENT

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)^2*n/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 this_sequence A068177 A099670 A006587

Adjacent sequences: A055300 A055301 A055302 this_sequence A055304 A055305 A055306

KEYWORD

nonn

AUTHOR

Christian G. Bower (bowerc(AT)usa.net), May 11 2000

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Last modified December 13 23:45 EST 2009. Contains 170824 sequences.


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