A290363 Number of 9-leaf rooted trees with n levels.

0, 1, 30, 424, 3357, 17836, 71769, 236093, 667335, 1676364, 3832477, 8113347, 16112746, 30319341, 54481246, 94072398, 156878210, 253719339, 399333792, 613438978, 921996699, 1358705458, 1966745847, 2800806163, 3929416785, 5437623230, 7430029191, 10034242245

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 (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Row n=9 of A290353.

Programs

Maple

a:= n-> (((((((1385*n+1124)*n+4018)*n+6776)*n+7945)*n
        +9716)*n+6812)*n+2544)*n/8!:
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[-(8*x^6 + 135*x^5 + 493*x^4 + 537*x^3 + 190*x^2 + 21*x + 1)*x/(x - 1)^9, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 14 2023 *)

Formula

G.f.: -(8*x^6+135*x^5+493*x^4+537*x^3+190*x^2+21*x+1)*x / (x-1)^9.

a(n) = (1385*n^8 +1124*n^7 +4018*n^6 +6776*n^5 +7945*n^4 +9716*n^3 +6812*n^2 +2544*n)/8!.