A014413 Triangular array formed from elements to right of middle of Pascal's triangle.

1, 1, 3, 1, 4, 1, 10, 5, 1, 15, 6, 1, 35, 21, 7, 1, 56, 28, 8, 1, 126, 84, 36, 9, 1, 210, 120, 45, 10, 1, 462, 330, 165, 55, 11, 1, 792, 495, 220, 66, 12, 1, 1716, 1287, 715, 286, 78, 13, 1, 3003, 2002, 1001, 364, 91, 14, 1, 6435, 5005, 3003, 1365, 455, 105, 15, 1

Offset: 1

Author

Mohammad K. Azarian

Keywords

• tabf
• nonn
• easy

Examples

			Triangle begins as:
    1;
    1;
    3,   1;
    4,   1;
   10,   5,   1;
   15,   6,   1;
   35,  21,   7,  1;
   56,  28,   8,  1;
  126,  84,  36,  9,  1;
  210, 120,  45, 10,  1;
  462, 330, 165, 55, 11, 1;
  792, 495, 220, 66, 12, 1;
  ...
		

Links

• Reinhard Zumkeller, Rows n = 1..200 of triangle, flattened

Crossrefs

Cf. A014462.

Cf. A007318, A034868, A034869, A265848.

Programs

Haskell

a014413 n k = a014413_tabf !! (n-1) !! (k-1)
a014413_row n = a014413_tabf !! (n-1)
a014413_tabf = [1] : f 1 [1] where
   f 0 us'@(_:us) = ys : f 1 ys where
                    ys = zipWith (+) us' (us ++ [0])
   f 1 vs@(v:_) = ys' : f 0 ys where
                  ys@(_:ys') = zipWith (+) (vs ++ [0]) ([v] ++ vs)
-- Reinhard Zumkeller, Dec 24 2015

Mathematica

Table[Binomial[n,k],{n,15},{k,Ceiling[(n+1)/2],n}]//Flatten  (* Stefano Spezia, Jan 16 2025 *)

Extensions

More terms from James Sellers