OFFSET
0,8
LINKS
Alois P. Heinz, Rows n = 0..55, flattened
Lun Lv, Zhihong Liu, Some Identities Related to Restricted Lattice Paths, 2016 9th International Symposium on Computational Intelligence and Design (ISCID), pp. 338-340.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 5, 3, 1, 1;
1, 14, 17, 4, 1, 1;
1, 42, 171, 43, 5, 1, 1;
1, 132, 3113, 1252, 89, 6, 1, 1;
1, 429, 106419, 104098, 5885, 161, 7, 1, 1;
1, 1430, 7035649, 25511272, 1518897, 20466, 265, 8, 1, 1;
This sequence formatted as a square array:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 2, 5, 14, 42, 132, 429, ...
1, 1, 3, 17, 171, 3113, 106419, 7035649, ...
1, 1, 4, 43, 1252, 104098, 25511272, 18649337311, ...
1, 1, 5, 89, 5885, 1518897, 1558435125, 6386478643785, ...
1, 1, 6, 161, 20466, 12833546, 40130703276, 627122621447281, ...
MAPLE
T:= proc(n, k) option remember; `if`(k=n, 1, add(
T(j+k, k)*T(n-j-1, k)*k^j, j=0..n-k-1))
end:
seq(seq(T(n, k), k=0..n), n=0..12); # Alois P. Heinz, Aug 10 2017
MATHEMATICA
nmax = 10; col[k_] := col[k] = Module[{A}, A[_] = 0; Do[A[x_] = Normal[1/(1 - x*A[k*x]) + O[x]^(nmax-k+1)], {nmax-k+1}]; CoefficientList[A[x], x]];
T[n_, k_] := col[k][[n-k+1]];
Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 05 2019, using g.f. given for column sequences *)
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Jan 20 2004, Oct 16 2008
STATUS
approved