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

1,4

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

Formula

Take Weigh transform of A038084 and shift right.

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 *)

Crossrefs

Cf. A038081-A038093.

Sequence in context: A029996 A294123 A321048 * A124313 A049890 A351915

Adjacent sequences: A038082 A038083 A038084 * A038086 A038087 A038088

Keyword

nonn,fini

Author

Christian G. Bower, Jan 04 1999

Status

approved