A038085 Number of n-node rooted identity trees of height at most 6.

1, 1, 1, 2, 3, 6, 12, 24, 45, 85, 157, 289, 529, 969, 1764, 3208, 5807, 10493, 18901, 33977, 60919, 109019, 194662, 346940, 617148, 1095884, 1942576, 3437834, 6074239, 10716076, 18877025, 33205498, 58328831, 102323302, 179267087, 313674445, 548183968

Offset: 1

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn
• fini

Comments

The number of terms is A038093(6), a number that is too large to write down!

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A038081-A038093.

Programs

Maple

weigh:= proc(p) proc(n) `if`(n<0, 1, coeff(mul((1+x^k)^p(k), k=1..n), x,n)) end end: wsh:= p-> n-> weigh(p)(n-1): a:= (wsh@@3)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..40);  # Alois P. Heinz, Sep 10 2008

Mathematica

Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 6] (* Geoffrey Critzer, Aug 01 2013 *)

Formula

Take Weigh transform of A038084 and shift right.