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

1,3

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A014462.

Cf. A007318, A034868, A034869, A265848.

Sequence in context: A180062 A340072 A079546 * A262072 A321743 A341766

Adjacent sequences: A014410 A014411 A014412 * A014414 A014415 A014416

Keyword

tabf,nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved