This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A028412 #41 Oct 31 2019 01:44:16
%S A028412 1,1,1,1,3,2,1,4,8,3,1,7,17,21,5,1,11,48,72,55,8,1,18,122,329,305,144,
%T A028412 13,1,29,323,1353,2255,1292,377,21,1,47,842,5796,15005,15456,5473,987,
%U A028412 34,1,76,2208,24447,104005,166408,105937,23184,2584,55,1,123,5777
%N A028412 Rectangular array of numbers Fibonacci(m(n+1))/Fibonacci(m), m >= 1, n >= 0, read by downward antidiagonals.
%C A028412 Every integer-valued quotient of two Fibonacci numbers is in this array. - _Clark Kimberling_, Aug 28 2008
%C A028412 Not only does 5 divide row 5, but 50 divides (-5 + row 5), as in A214984. - _Clark Kimberling_, Nov 02 2012
%D A028412 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 142.
%H A028412 Clark Kimberling, <a href="/A028412/b028412.txt">Table of n, a(n) for n = 0..1829</a>
%H A028412 I. Strazdins, <a href="http://dx.doi.org/10.1007/978-94-011-5020-0_44">Lucas factors and a Fibonomial generating function</a>, in Applications of Fibonacci numbers, Vol. 7 (Graz, 1996), 401-404, Kluwer Acad. Publ., Dordrecht, 1998.
%F A028412 T(n, m) = Sum_{i_1>=0} Sum_{i_2>=0} ... Sum_{i_m>=0} C(n-i_m, i_1)*C(n-i_1, i_2)*C(n-i_2, i_3)*...*C(n-i_{m-1}, i_m).
%F A028412 G.f. for column m >= 1: 1/(1 - Lucas(m)*x + (-1)^m*x^2), where Lucas(m) = A000204(m). - _Paul D. Hanna_, Jan 28 2012
%e A028412 1 1 1 1 1 1
%e A028412 1 3 4 7 11 18
%e A028412 2 8 17 48 122 323
%e A028412 3 21 72 329 1353 5796
%e A028412 5 55 305 2255 15005 104005
%e A028412 8 144 1292 15456 166408 1866294
%e A028412 13 377 5473 105937 1845493 33489287
%e A028412 ...
%t A028412 max = 11; col[m_] := CoefficientList[ Series[ 1/(1 - LucasL[m]*x + (-1)^m*x^2), {x, 0, max}], x]; t = Transpose[ Table[ col[m], {m, 1, max}]] ; Flatten[ Table[ t[[n - m + 1, m]], {n, 1, max }, {m, n, 1, -1}]] (* _Jean-François Alcover_, Feb 21 2012, after _Paul D. Hanna_ *)
%t A028412 f[n_] := Fibonacci[n]; t[m_, n_] := f[m*n]/f[n]
%t A028412 TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]] (* array *)
%t A028412 t = Flatten[Table[t[k, n + 1 - k], {n, 1, 120}, {k, 1, n}]] (* sequence *) (* _Clark Kimberling_, Nov 02 2012 *)
%o A028412 (PARI) {T(n,m)=polcoeff(1/(1 - Lucas(m)*x + (-1)^m*x^2 +x*O(x^n)),n)}
%Y A028412 Columns include A000045, A001906, A001076, A004187, A049666, A049660, A049667, A049668, A049669, A049670.
%Y A028412 Rows include (essentially) A000032, A047946, A083564, A103226.
%Y A028412 Main diagonal is A051294.
%Y A028412 Transpose is A214978.
%K A028412 nonn,tabl,easy,nice
%O A028412 0,5
%A A028412 _N. J. A. Sloane_
%E A028412 More terms from _Erich Friedman_, Jun 03 2001
%E A028412 Edited by _Ralf Stephan_, Feb 03 2005
%E A028412 Better description from _Clark Kimberling_, Aug 28 2008