A038086 Number of n-node rooted identity trees of height at most 7.

1, 1, 1, 2, 3, 6, 12, 25, 51, 105, 211, 421, 832, 1641, 3224, 6328, 12382, 24200, 47197, 91915, 178683, 346897, 672443, 1301850, 2517078, 4860938, 9376300, 18066270, 34772627, 66859667, 128427832, 246456677, 472519632, 905131358, 1732313955, 3312661001

Offset

1,4

Comments

The number of terms is A038093(7), a number that is too large to write down!

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 A038085 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@@4)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..40);  # Alois P. Heinz, Sep 10 2008

Mathematica

Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 7] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

Cf. A038081-A038093.

Sequence in context: A187741 A216632 A077903 * A032305 A032218 A005829

Adjacent sequences: A038083 A038084 A038085 * A038087 A038088 A038089

Keyword

nonn,fini

Author

Christian G. Bower, Jan 04 1999

Status

approved