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

%I A014413 #17 Jul 02 2025 16:01:55
%S A014413 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 A014413 45,10,1,462,330,165,55,11,1,792,495,220,66,12,1,1716,1287,715,286,78,
%U A014413 13,1,3003,2002,1001,364,91,14,1,6435,5005,3003,1365,455,105,15,1
%N A014413 Triangular array formed from elements to right of middle of Pascal's triangle.
%H A014413 Reinhard Zumkeller, <a href="/A014413/b014413.txt">Rows n = 1..200 of triangle, flattened</a>
%e A014413 Triangle begins as:
%e A014413     1;
%e A014413     1;
%e A014413     3,   1;
%e A014413     4,   1;
%e A014413    10,   5,   1;
%e A014413    15,   6,   1;
%e A014413    35,  21,   7,  1;
%e A014413    56,  28,   8,  1;
%e A014413   126,  84,  36,  9,  1;
%e A014413   210, 120,  45, 10,  1;
%e A014413   462, 330, 165, 55, 11, 1;
%e A014413   792, 495, 220, 66, 12, 1;
%e A014413   ...
%t A014413 Table[Binomial[n,k],{n,15},{k,Ceiling[(n+1)/2],n}]//Flatten  (* _Stefano Spezia_, Jan 16 2025 *)
%o A014413 (Haskell)
%o A014413 a014413 n k = a014413_tabf !! (n-1) !! (k-1)
%o A014413 a014413_row n = a014413_tabf !! (n-1)
%o A014413 a014413_tabf = [1] : f 1 [1] where
%o A014413    f 0 us'@(_:us) = ys : f 1 ys where
%o A014413                     ys = zipWith (+) us' (us ++ [0])
%o A014413    f 1 vs@(v:_) = ys' : f 0 ys where
%o A014413                   ys@(_:ys') = zipWith (+) (vs ++ [0]) ([v] ++ vs)
%o A014413 -- _Reinhard Zumkeller_, Dec 24 2015
%Y A014413 Cf. A014462.
%Y A014413 Cf. A007318, A034868, A034869, A265848.
%K A014413 tabf,nonn,easy
%O A014413 1,3
%A A014413 _Mohammad K. Azarian_
%E A014413 More terms from _James Sellers_