A007715 Number of 5-leaf rooted trees with n levels.

1, 7, 27, 75, 170, 336, 602, 1002, 1575, 2365, 3421, 4797, 6552, 8750, 11460, 14756, 18717, 23427, 28975, 35455, 42966, 51612, 61502, 72750, 85475, 99801, 115857, 133777, 153700, 175770, 200136, 226952, 256377, 288575, 323715, 361971, 403522, 448552, 497250

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• easy

Examples

			a(7) = 7*28 - (7*0+4*1+1*3-2*6-5*10-8*15-11*21) = 602. - _Bruno Berselli_, Jun 22 2013
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
• Index entries for sequences related to rooted trees
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Row n=5 of A290353.

Programs

Magma

[n*(n+1)*(5*n^2+n+6)/24: n in [1..45]]; // Vincenzo Librandi, Jul 21 2011

Mathematica

Table[n(n+1)(5n^2+n+6)/24,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{1,7,27,75,170},40] (* Harvey P. Dale, Jul 20 2011 *)

Formula

Expansion of x*(1+2x+2x^2)/(1-x)^5.

a(n) = n*(n+1)*(5*n^2+n+6)/24. - T. D. Noe, Feb 09 2007

a(1)=1, a(2)=7, a(3)=27, a(4)=75, a(5)=170, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Jul 20 2011

a(n) = n*A000217(n) - sum((n-3*i)*A000217(i), i=0..n-1). - Bruno Berselli, Jun 22 2013