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%I #49 Jul 24 2019 05:06:39
%S 1,1,1,1,2,1,1,3,3,1,1,5,7,4,1,1,7,14,12,5,1,1,9,25,30,18,6,1,1,12,42,
%T 66,55,26,7,1,1,15,66,132,143,91,35,8,1,1,18,99,245,334,273,140,45,9,
%U 1,1,22,143,429,715,728,476,204,57,10,1
%N Triangle read by rows: T(i,j) = integer part of binomial(i+j, i-j)/(2*j+1) for i >= 1 and j = 0..i-1.
%C In the Loh-Shannon-Horadam paper, Table 3 contains a typo (see Extensions lines).
%C T(n,k) = round(A258993(n,k)/(2*k+1)). - _Reinhard Zumkeller_, Jun 22 2015
%C From _Reinhard Zumkeller_, Jun 23 2015: (Start)
%C (using tables 4 and 5 of the Loh-Shannon-Horadam paper, p. 8f).
%C T(n, n-1) = 1;
%C T(n, n-2) = n for n > 1;
%C T(n, n-3) = A000969(n-3) for n > 2;
%C T(n, n-4) = A000330(n-3) for n > 3;
%C T(n, n-5) = T(2*n-7, 2) = A000970(n) for n > 4;
%C T(n, n-6) = A000971(n) for n > 5;
%C T(n, n-7) = A000972(n) for n > 6;
%C T(n, n-8) = A000973(n) for n > 7;
%C T(n, 1) = A001840(n-1) for n > 1;
%C T(2*n, n) = A001764(n);
%C T(3*n-1, 1) = A000326(n);
%C T(3*n, 2*n) = A002294(n);
%C T(4*n, 3*n) = A002296(n). (End)
%H Reinhard Zumkeller, <a href="/A258708/b258708.txt">Rows n = 1..125 of triangle, flattened</a>
%H R. P. Loh, A. G. Shannon, and A. F. Horadam, <a href="/A000969/a000969.pdf">Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients</a>, Preprint, 1980.
%e Triangle T(i, j) (with rows i >= 1 and columns j >= 0) begins as follows:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 3, 1;
%e 1, 5, 7, 4, 1;
%e 1, 7, 14, 12, 5, 1;
%e 1, 9, 25, 30, 18, 6, 1;
%e 1, 12, 42, 66, 55, 26, 7, 1;
%e 1, 15, 66, 132, 143, 91, 35, 8, 1;
%e 1, 18, 99, 245, 334, 273, 140, 45, 9, 1;
%e ...
%o (Haskell)
%o a258708 n k = a258708_tabl !! (n-1) !! k
%o a258708_row n = a258708_tabl !! (n-1)
%o a258708_tabl = zipWith (zipWith ((round .) . ((/) `on` fromIntegral)))
%o a258993_tabl a158405_tabl
%o -- _Reinhard Zumkeller_, Jun 22 2015, Jun 16 2015
%Y Cf. A011793.
%Y Cf. A007318, A258993, A158405, A005408, A006013 (central terms).
%Y Cf. A000326, A000330, A000969, A000970, A000971, A000972, A000973, A000976, A001764, A001840, A002294, A002296.
%K nonn,tabl
%O 1,5
%A _N. J. A. Sloane_, Jun 12 2015
%E Corrected T(8,5) = 26 from _Reinhard Zumkeller_, Jun 13 2015
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