OFFSET
0,9
LINKS
M. Bousquet-Mélou, Limit laws for embedded trees, arXiv:math/0501266 [math.CO], 2005.
FORMULA
EXAMPLE
1, 1, 1, 2, 4, 10, 26, 73, 213, 645, ...
1, 1, 2, 4, 10, 26, 73, 213, 645, 2007, ...
1, 1, 2, 5, 13, 37, 109, 334, 1050, 3377, ...
1, 1, 2, 5, 14, 41, 126, 398, 1289, 4253, ...
1, 1, 2, 5, 14, 42, 131, 422, 1390, 4664, ...
1, 1, 2, 5, 14, 42, 132, 428, 1422, 4812, ...
1, 1, 2, 5, 14, 42, 132, 429, 1429, 4853, ...
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4861, ...
MATHEMATICA
nmax = 11;
b[t_] = Sum[Binomial[2n, n]/(n + 1) t^n, {n, 0, nmax}] ;
c[t_] = 1; Do[c[t_] = t (1 + c[t]^2)^2/(1 - c[t] + c[t]^2) + O[t]^(nmax + 1), {nmax + 1}];
a[n_, t_] := a[n, t] = b[t] (1 - c[t]^(n + 2)) ((1 - c[t]^(n + 7))/((1 - c[t]^(n + 4)) (1 - c[t]^(n + 5)))) + O[t]^(nmax + 1);
T[n_, k_] := SeriesCoefficient[a[n, t], {t, 0, k}];
Table[T[n - k, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 25 2018 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ralf Stephan, Jan 21 2005
STATUS
approved