A290362 Number of 8-leaf rooted trees with n levels.

0, 1, 22, 223, 1344, 5727, 19193, 54046, 133476, 297633, 611644, 1175845, 2138500, 3711279, 6187767, 9965276, 15570232, 23687409, 35193282, 51193771, 73066648, 102508879, 141589173, 192806010, 259151420, 344180785, 452088936, 587792817, 757020988, 966410239

Offset: 0

Author

Alois P. Heinz, Jul 28 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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 linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Row n=8 of A290353.

Programs

Maple

a:= n-> ((((((272*n+273)*n+749)*n+1365)*n+1043)*n+882)*n+456)*n/7!:
seq(a(n), n=0..40);

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,22,223,1344,5727,19193,54046},30] (* Harvey P. Dale, Oct 16 2017 *)

Formula

G.f.: (5*x^5+57*x^4+120*x^3+75*x^2+14*x+1)*x / (x-1)^8.

a(n) = (272*n^7+273*n^6+749*n^5+1365*n^4+1043*n^3+882*n^2+456*n)/7!.