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

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn
• fini
• full

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

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(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 *)

Formula

Take Weigh transform of A038082 and shift right.