OFFSET
0,5
COMMENTS
LINKS
Wolfdieter Lang, First 10 rows.
FORMULA
EXAMPLE
Triangle starts:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 9, 11, 4, 1;
1, 23, 51, 22, 5, 1;
1, 65, 275, 157, 37, 6, 1;
...
MATHEMATICA
col[m_] := col[m] = CatalanNumber[#]*m^#& /@ Range[0, 20] // Accumulate;
T[n_, m_] := If[m == 0, 1, col[m][[n - m + 1]]];
Table[T[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Aug 29 2022 *)
PROG
(PARI) t(n, m) = if (m==0, 1, if (n==m, 1, sum(kk=0, n-m, m^kk*binomial(2*kk, kk)/(kk+1))));
tabl(nn) = {for (n=0, nn, for (m=0, n, print1(t(n, m), ", "); ); print(); ); } \\ Michel Marcus, Nov 25 2015
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Oct 31 2005
STATUS
approved