A086864 a(n) = (n-1)*(n-2)*(n-3)*(3*n-10)*3^(n-5)/4.

0, 0, 0, 1, 30, 360, 2970, 19845, 115668, 612360, 3018060, 14073345, 62788770, 270208224, 1128426390, 4594307445, 18302828040, 71553216240, 275154640632, 1042806816225, 3901324324230, 14427539010360, 52801538445810, 191427950399301, 688082033693340

Offset: 1

Author

N. J. A. Sloane, Sep 16 2003

Keywords

• nonn
• easy

References

• L. Ericson et al., Enumeration of tree properties..., Algorithms Review, 1 (1990), 119-124.

Links

• Index entries for linear recurrences with constant coefficients, signature (15,-90,270,-405,243).

Programs

Mathematica

Table[((n-1)(n-2)(n-3)(3n-10)3^(n-5))/4,{n,30}] (* or *) LinearRecurrence[ {15,-90,270,-405,243},{0,0,0,1,30},30] (* Harvey P. Dale, May 15 2015 *)

Formula

G.f.: x^4*(15*x+1)/(1-3*x)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]

a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=30, a(n)=15*a(n-1)-90*a(n-2)+ 270*a(n-3)- 405*a(n-4)+243*a(n-5). - Harvey P. Dale, May 15 2015

a(n) = A036217(n-4)+15*A036217(n-5). - R. J. Mathar, Apr 14 2018

Extensions

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

Definition clarified by Harvey P. Dale, May 15 2015