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A258708 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.

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