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%I #13 Sep 08 2022 08:45:50
%S 1,1,1,1,2,1,1,3,2,1,1,2,6,2,1,1,3,10,5,1,1,1,2,8,20,8,2,1,1,2,11,35,
%T 18,5,1,1,1,1,6,28,70,28,6,1,1,1,1,8,42,126,63,17,4,1,1,1,1,5,24,105,
%U 252,105,24,5,1,1,1,1,6,33,165,462,231,66,17,4,1,1,1,1,4,22,99,396,924,396,99,22,4,1,1
%N Triangle, read by rows: T(n, k) = ceiling( binomial(n, k)/(1 + (k - floor(n/2))^2) ).
%C Row sums are: {1, 2, 4, 7, 12, 21, 42, 74, 142, 264, 524, ...}.
%H G. C. Greubel, <a href="/A172279/b172279.txt">Rows n = 0..100 of triangle, flattened</a>
%F T(n, k) = ceiling( binomial(n, k)/((1 + (k - floor(n/2))^2)).
%F T(2*n, n) = binomial(2*n,n) (cf. A000984). - _Michel Marcus_, May 22 2019
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 2, 1;
%e 1, 2, 6, 2, 1;
%e 1, 3, 10, 5, 1, 1;
%e 1, 2, 8, 20, 8, 2, 1;
%e 1, 2, 11, 35, 18, 5, 1, 1;
%e 1, 1, 6, 28, 70, 28, 6, 1, 1;
%e 1, 1, 8, 42, 126, 63, 17, 4, 1, 1;
%e 1, 1, 5, 24, 105, 252, 105, 24, 5, 1, 1;
%t T[n_,k_]:= Ceiling[Binomial[n,k]/(1+(k-Floor[n/2])^2)];
%t Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
%o (PARI)
%o {T(n, k) = ceil(binomial(n, k)/(1 + (k -floor(n/2))^2))};
%o for(n=0, 12, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 21 2019
%o (Magma)
%o T:= func< n,k | Ceiling(Binomial(n, k)/(1 + (k - Floor(n/2))^2)) >;
%o [[T(n,k) : k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, May 21 2019
%o (Sage)
%o def T(n, k): return ceil(binomial(n, k)/(1 + (k -floor(n/2))^2))
%o [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, May 21 2019
%Y Cf. A000984 (central binomial coefficients).
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Jan 30 2010
%E Edited by _G. C. Greubel_, May 21 2019
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