A038087 Number of n-node rooted identity trees of height at most 8.

1, 1, 1, 2, 3, 6, 12, 25, 52, 112, 238, 503, 1053, 2194, 4547, 9406, 19401, 39965, 82189, 168837, 346380, 709917, 1453380, 2972636, 6074138, 12400794, 25295272, 51556337, 104998985, 213681811, 434548933, 883104930, 1793484049, 3640032699, 7383188993

Offset

1,4

Comments

A finite sequence with a very large number of terms, A038093(8). The sum of all terms is 2^(2^(2^(2^65536))).

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 A038086 and shift right.

Maple

weigh:= proc(p) proc(n) local x, k; coeff(series(mul((1+x^k)^p(k), k=1..n), x, n+1), x, n) end end: wsh:= p-> n-> weigh(p)(n-1): a:= (wsh@@5)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..33);  # Alois P. Heinz, Sep 10 2008

Mathematica

Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 8] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

Cf. A038081-A038093.

Sequence in context: A032305 A032218 A005829 * A116379 A116380 A004111

Adjacent sequences: A038084 A038085 A038086 * A038088 A038089 A038090

Keyword

nonn,fini

Author

Christian G. Bower, Jan 04 1999

Status

approved