OFFSET
0,3
LINKS
M. Bousquet-Mélou, Limit laws for embedded trees, arXiv:math/0501266 [math.CO], 2005.
FORMULA
EXAMPLE
1,2,9,54,378,2916,24057,208494,1876446,17399772,
1,3,17,119,932,7838,69275,635279,5994584,57872666,
1,3,18,134,1111,9833,90959,868827,8504314,84866778,
1,3,18,135,1133,10176,95635,928442,9236144,93646430,
1,3,18,135,1134,10205,96191,937361,9365984,95427597,
1,3,18,135,1134,10206,96227,938179,9381050,95673739,
1,3,18,135,1134,10206,96228,938222,9382179,95697199,
1,3,18,135,1134,10206,96228,938223,9382229,95698688,
MATHEMATICA
nmax = 9;
b[t_] = 2/(1 + Sqrt[1 - 12t]) + O[t]^(nmax+1);
c[t_] = (1 + Sqrt[1 - 12t] - t (8 + Sqrt[2] Sqrt[(1 + Sqrt[1 - 12t] - 2 (7 + 4 Sqrt[1 - 12t]) t + 24t^2)/t^2]))/(4t) + O[t]^(nmax+1) // Simplify[#, t > 0]&;
a[n_, t_] := a[n, t] = b[t] (1 - c[t]^(n + 1)) (1 - c[t]^(n + 4))/((1 - c[t]^(n+2)) (1 - c[t]^(n+3))) + O[t]^(nmax+1) // Simplify[#, t > 0]&;
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