A290361 Number of 7-leaf rooted trees with n levels.

0, 1, 15, 111, 518, 1789, 5026, 12166, 26328, 52221, 96613, 168861, 281502, 450905, 697984, 1048972, 1536256, 2199273, 3085467, 4251307, 5763366, 7699461, 10149854, 13218514, 17024440, 21703045, 27407601, 34310745, 42606046, 52509633, 64261884, 78129176

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 sequences related to rooted trees
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Row n=7 of A290353.

Programs

Maple

a:= n-> (((((61*n+69)*n+145)*n+195)*n+154)*n+96)*n/6!:
seq(a(n), n=0..40);

Formula

G.f.: -(4*x^4+21*x^3+27*x^2+8*x+1)*x / (x-1)^7.

a(n) = (61*n^6+69*n^5+145*n^4+195*n^3+154*n^2+96*n)/6!.