OFFSET
1,3
LINKS
Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 183.
FORMULA
E.g.f. satisfies: A(x,y) = x exp(A(x,y)) - x^2 + y x^2.
EXAMPLE
Triangle begins
1,
0, 2,
3, 6,
16, 48,
145, 420, 60,
1536, 4800, 1440,
19579, 65730, 31500, 840,
290816, 1053696, 698880, 53760,
...
T(3,1)=6 because there are 6 labeled rooted trees (paths) o-o-o and these 6 trees have 1 vertex whose only descendent is a leaf. T(3,0) = 3 because there are 3 labeled trees of the form
o
/ \
o o
and these 3 trees have no such vertices.
MATHEMATICA
nn = 10; Range[0, nn]! CoefficientList[Series[-z^2 + u z^2 - ProductLog[-E^((-1 + u) z^2) z], {z, 0, nn}], {z, u}] // Grid
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Mar 26 2017
STATUS
approved