A038088 Number of n-node rooted identity trees of height 4.

1, 3, 5, 8, 12, 17, 23, 32, 41, 52, 66, 83, 102, 124, 152, 181, 216, 255, 299, 346, 400, 458, 521, 588, 659, 735, 814, 896, 979, 1067, 1151, 1239, 1324, 1407, 1486, 1564, 1635, 1700, 1759, 1809, 1853, 1887, 1912, 1925, 1932, 1925, 1912, 1887, 1853

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..97

Index entries for sequences related to rooted trees

Formula

a(n) = A038083(n) - A038082(n).

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(f)-f: seq(a(n), n=5..97); # 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[4]-PadRight[f[3], Length[f[4]]], 4] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

Cf. A038081-A038093.

Column k=4 of A227819.

Sequence in context: A023544 A133263 A238531 * A018917 A167385 A265061

Adjacent sequences: A038085 A038086 A038087 * A038089 A038090 A038091

Keyword

nonn,fini,full

Author

Christian G. Bower, Jan 04 1999

Status

approved