A014413 - OEIS

%I #16 Jan 16 2025 16:22:37

%S 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,

%T 45,10,1,462,330,165,55,11,1,792,495,220,66,12,1,1716,1287,715,286,78,

%U 13,1,3003,2002,1001,364,91,14,1,6435,5005,3003,1365,455,105,15,1

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

%H Reinhard Zumkeller, <a href="/A014413/b014413.txt">Rows n = 1..200 of triangle, flattened</a>

%e Triangle begins as:

%e     1;

%e     1;

%e     3,   1;

%e     4,   1;

%e    10,   5,   1;

%e    15,   6,   1;

%e    35,  21,   7,  1;

%e    56,  28,   8,  1;

%e   126,  84,  36,  9,  1;

%e   210, 120,  45, 10,  1;

%e   462, 330, 165, 55, 11, 1;

%e   792, 495, 220, 66, 12, 1;

%e   ...

%t Table[Binomial[n,k],{n,15},{k,Ceiling[(n+1)/2],n}]//Flatten  (* _Stefano Spezia_, Jan 16 2025 *)

%o (Haskell)

%o a014413 n k = a014413_tabf !! (n-1) !! (k-1)

%o a014413_row n = a014413_tabf !! (n-1)

%o a014413_tabf = [1] : f 1 [1] where

%o    f 0 us'@(_:us) = ys : f 1 ys where

%o                     ys = zipWith (+) us' (us ++ [0])

%o    f 1 vs@(v:_) = ys' : f 0 ys where

%o                   ys@(_:ys') = zipWith (+) (vs ++ [0]) ([v] ++ vs)

%o -- _Reinhard Zumkeller_, Dec 24 2015

%Y Cf. A014462.

%Y Cf. A007318, A034868, A034869, A265848.

%K tabf,nonn,easy

%O 1,3

%A _Mohammad K. Azarian_

%E More terms from _James A. Sellers_