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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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

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

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Last modified September 28 19:57 EDT 2021. Contains 347717 sequences. (Running on oeis4.)