OFFSET
0,4
LINKS
Laurent Méhats, Lutz Straßburger, Non-crossing Tree Realizations of Ordered Degree Sequences, Pages 211-227 in Logical Aspects of Computational Linguistics. Celebrating 20 Years of LACL (1996-2016), 9th International Conference, LACL 2016, Nancy, France, December 5-7, 2016, Proceedings, Lecture Notes in Computer Science book series (LNCS, volume 10054). See Eq. (7).
EXAMPLE
Triangle begins:
1,
1,1,
2,3,2,
5,9,9,5,
14,28,34,28,14,
42,90,123,123,90,42,
132,297,440,497,440,297,132,
...
MAPLE
A000108 := proc(q)
if q <0 then
0;
else
binomial(2*q, q)/(1+q) ;
end if;
end proc:
R := proc(q, s)
option remember;
local a, j, l ;
if q= 0 then
A000108(s) ;
elif s = 0 then
A000108(q) ;
else
a := 0 ;
for j from 0 to q do
for l from 0 to s do
if j+l-1 >= 0 then
a := a+A000108(j+l-1) *procname(q-j, s-l) ;
end if;
end do:
end do:
end if;
end proc:
A293944 := proc(n, k)
R(n-k, k) ;
end proc:
seq(seq(A293944(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Nov 02 2017
MATHEMATICA
R[q_, s_] := R[q, s] = Module[{a, j, l}, If[q == 0, CatalanNumber[s], If[s == 0, CatalanNumber[q], a = 0; For[j = 0, j <= q, j++, For[l = 0, l <= s , l++, If[j + l - 1 >= 0, a = a + CatalanNumber[j + l - 1] R[q - j, s - l]] ]]]] /. Null -> a];
T [n_, k_] := R[n - k, k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 07 2020, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Oct 21 2017
EXTENSIONS
More terms from R. J. Mathar, Nov 02 2017
STATUS
approved