A220233 Triangular array read by rows. T(n,k) is the number of labeled rooted trees of height at most 2 with exactly k leaves at a distance 1 from the root, n>=1, 0<=k<=n-1.

0, 0, 2, 6, 0, 3, 12, 24, 0, 4, 80, 60, 60, 0, 5, 390, 480, 180, 120, 0, 6, 2352, 2730, 1680, 420, 210, 0, 7, 15176, 18816, 10920, 4480, 840, 336, 0, 8, 106416, 136584, 84672, 32760, 10080, 1512, 504, 0, 9, 801450, 1064160, 682920, 282240, 81900, 20160, 2520, 720, 0, 10

Offset

1,3

Comments

Row sums = A052512 for n>1. Column for k=0 is A220232.

Links

Table of n, a(n) for n=1..55.

Formula

E.g.f.: x*(exp(x*(exp(x) -1 + y)) - 1 + y) (letting T(1,1)=1).

Example

Triangle T(n,k) begins:
     0;
     0,    2;
     6,    0,    3;
    12,   24,    0,   4;
    80,   60,   60,   0,   5;
   390,  480,  180, 120,   0, 6;
  2352, 2730, 1680, 420, 210, 0, 7;
  ...

Mathematica

nn=7; f[list_]:=Select[list, #>0&]; a=x (Exp[x]-1+y); Prepend[Drop[Map[Insert[#, 0, -2]&, Map[f, Range[0, nn]!CoefficientList[Series[x (Exp[a]-1+y), {x, 0, nn}], {x, y}]]], 2], {0}]//Grid

Crossrefs

Sequence in context: A232178 A016590 A079461 * A084897 A021388 A011040

Adjacent sequences: A220230 A220231 A220232 * A220234 A220235 A220236

Keyword

nonn,tabl

Author

Geoffrey Critzer, Dec 08 2012

Status

approved