A038083 Number of n-node rooted identity trees of height at most 4.

1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 24, 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

1,4

Comments

A finite sequence with A038093(4) = 97 terms.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..97

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Formula

Take Weigh transform of A038082 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(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..97); # Alois P. Heinz, Sep 10 2008

Mathematica

a = Drop[CoefficientList[ Series[x (1 + x) (1 + x^2) (1 + x^3) (1 + x^4), {x, 0, 11}], x], 1]; nn = 97; Drop[ CoefficientList[ Series[x Product[(1 + x^i)^a[[i]], {i, 1, 11}], {x, 0, nn}], x], 1] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

Cf. A038081-A038093.

Sequence in context: A239883 A332283 A088318 * A238863 A060688 A005691

Adjacent sequences: A038080 A038081 A038082 * A038084 A038085 A038086

Keyword

nonn,fini,full

Author

Christian G. Bower, Jan 04 1999

Status

approved