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A133386 Number of forests of labeled rooted trees with n nodes, containing exactly 2 trees of height one, all others having height zero. 3
0, 0, 0, 0, 12, 120, 750, 3780, 16856, 69552, 272250, 1026300, 3762132, 13498056, 47615750, 165683700, 570024240, 1942538592, 6566094450, 22038141420, 73510278380, 243854707320, 804962754750, 2645408201700, 8658857196552, 28237920483600, 91778694166250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..650

A. P. Heinz, Finding Two-Tree-Factor Elements of Tableau-Defined Monoids in Time O(n^3), Ed. S. G. Akl, F. Fiala, W. W. Koczkodaj: Advances in Computing and Information, ICCI90 Niagara Falls, LNCS 468, Springer-Verlag (1990), pp. 120-128.

Index entries for linear recurrences with constant coefficients, signature (18,-141,630,-1767,3222,-3815,2826,-1188,216).

FORMULA

a(n) = n*(n-1) * Stirling2(n-1,3).

G.f.: -2*x^4*(85*x^4-180*x^3+141*x^2-48*x+6) / ((x-1)^3*(3*x-1)^3*(2*x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=12, a(5)=120, a(6)=750, a(7)=3780, a(8)=16856, a(n)=18*a(n-1)-141*a(n-2)+630*a(n-3)-1767*a(n-4)+ 3222*a(n-5)- 3815*a(n-6)+2826*a(n-7)-1188*a(n-8)+216*a(n-9). - Harvey P. Dale, May 02 2015

EXAMPLE

a(4) = 12 because 12 trees of the given kind exist: 1<-3 2<-4, 1<-4 2<-3, 1<-2 3<-4, 1<-4 3<-2, 1<-2 4<-3, 1<-3 4<-2, 2<-1 3<-4, 2<-4 3<-1, 2<-1 4<-3, 2<-3 4<-1, 3<-1 4<-2 and 3<-2 4<-1.

MAPLE

a:= n-> n*(n-1)*Stirling2(n-1, 3):

seq(a(n), n=0..50);

MATHEMATICA

Join[{0}, Table[n(n-1)StirlingS2[n-1, 3], {n, 30}]] (* or *) LinearRecurrence[{18, -141, 630, -1767, 3222, -3815, 2826, -1188, 216}, {0, 0, 0, 0, 12, 120, 750, 3780, 16856}, 30] (* Harvey P. Dale, May 02 2015 *)

CROSSREFS

Cf. A058877, A000248.

Column k=2 of A133399.

Column 2 of A198204. - Peter Bala, Aug 01 2012

Sequence in context: A188251 A093334 A001816 * A305624 A056320 A056311

Adjacent sequences:  A133383 A133384 A133385 * A133387 A133388 A133389

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 22 2007

STATUS

approved

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Last modified August 19 21:19 EDT 2019. Contains 326133 sequences. (Running on oeis4.)