OFFSET
1,2
COMMENTS
Row 1, (1,2,3,4,5,...)**(1,2,6,20,70,...):
Row 2, (1,2,3,4,5,...)**(2,6,20,70,252,...):
Row 3, (1,2,3,4,5,...)**(6,20,70,252,...):
For a guide to related arrays, see A213500.
LINKS
Clark Kimberling, Antidiagonals n = 1..60, flattened
EXAMPLE
Northwest corner (the array is read by falling antidiagonals):
1....4.....13.....42.....141
2....10....38.....136....486
6....32....128....476....1748
20...110...452....1718...6416
70...392...1638...6316...23864
MATHEMATICA
b[n_]:=n; c[n_]:=Binomial[2n-2, n-1
t[n_, k_]:=Sum[b[k-i]c[n+i], {i, 0, k-1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n-k+1, k], {n, 12}, {k, n, 1, -1}]]
r[n_]:=Table[t[n, k], {k, 1, 20}] (* A213853 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jul 05 2012
STATUS
approved