A038084 Number of n-node rooted identity trees of height at most 5.

1, 1, 1, 2, 3, 6, 11, 19, 31, 52, 85, 140, 228, 370, 594, 954, 1519, 2412, 3814, 6006, 9419, 14726, 22938, 35612, 55125, 85065, 130900, 200875, 307446, 469342, 714784, 1085956, 1646160, 2489838, 3757929, 5660110, 8508224, 12764585, 19114360, 28570525, 42629077

Offset

1,4

Comments

A finite sequence with A038093(5) = 3211265 terms.

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 A038083 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@@2)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..50); # Alois P. Heinz, Sep 10 2008

Mathematica

Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x]&, {1}, 5] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

Cf. A038081-A038093.

Sequence in context: A288583 A090036 A024971 * A018169 A238644 A191629

Adjacent sequences: A038081 A038082 A038083 * A038085 A038086 A038087

Keyword

nonn,fini

Author

Christian G. Bower, Jan 04 1999

Status

approved