A038089 Number of n-node rooted identity trees of height 5.

1, 4, 9, 18, 34, 61, 108, 187, 318, 528, 871, 1417, 2288, 3662, 5825, 9203, 14471, 22639, 35266, 54725, 84607, 130379, 200287, 306787, 468607, 713970, 1085060, 1645181, 2488771, 3756778, 5658871, 8506900, 12763178, 19112874, 28568961, 42627442, 63493739

Offset

6,2

Comments

The number of terms with a(n)>0 is A038093(5)-5 = 3211260. - Alois P. Heinz, Sep 22 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Index entries for sequences related to rooted trees

Formula

A038084 - A038083.

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): f:= n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0): a:= (wsh@@2)(f)-wsh(f): seq(a(n), n=6..40);  # Alois P. Heinz, Sep 10 2008

Mathematica

f[n_]:=Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 50}], x]&, {1}, n]; Drop[f[5]-PadRight[f[4], Length[f[5]]], 5] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

Cf. A038081-A038093.

Column k=5 of A227819.

Sequence in context: A019454 A019453 A301104 * A333394 A301150 A301078

Adjacent sequences: A038086 A038087 A038088 * A038090 A038091 A038092

Keyword

nonn,fini

Author

Christian G. Bower, Jan 04 1999

Status

approved