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

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn
• fini

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

Crossrefs

Cf. A038081-A038093.

Programs

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 *)

Formula

Take Weigh transform of A038083 and shift right.