A290364 Number of 10-leaf rooted trees with n levels.

0, 1, 42, 817, 8429, 55627, 268272, 1030101, 3331117, 9425128, 23970089, 55880968, 121188860, 247272012, 478904297, 886654486, 1578265414, 2713745819, 4525019252, 7341094011, 11619845543, 17987638185, 27288156478, 40641967587, 59518495595, 85822255610

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Row n=10 of A290353.

Programs

Maple

a:= n-> ((((((((7936*n+4635)*n+24756)*n+43974)*n+65352)*n
         +60795)*n+81524)*n+72036)*n+1872)*n/9!:
seq(a(n), n=0..40);

Mathematica

LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0,1,42,817,8429,55627,268272,1030101,3331117,9425128},30] (* Harvey P. Dale, Jan 09 2019 *)

Formula

G.f.: (13*x^7+312*x^6+1835*x^5+3272*x^4+2029*x^3+442*x^2+32*x+1)*x / (x-1)^10.

a(n) = (7936*n^9 +4635*n^8 +24756*n^7 +43974*n^6 +65352*n^5 +60795*n^4 +81524*n^3 +72036*n^2 +1872*n)/9!.