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A172350 Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=5.

%I A172350 #4 Jul 05 2012 11:38:42
%S A172350 1,1,1,1,1,1,1,6,6,1,1,11,66,11,1,1,41,451,451,41,1,1,96,3936,7216,
%T A172350 3936,96,1,1,301,28896,197456,197456,28896,301,1,1,781,235081,3761296,
%U A172350 14019376,3761296,235081,781,1,1,2286,1785366,89565861,781665696
%N A172350 Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=5.
%C A172350 Start from the generalized Fibonacci sequence A015440 and its partial products c(n) = 1, 1, 1, 6, 66, 2706, 259776, 78192576, 61068401856, 139602366642816...  Then t(n,k) = c(n)/(c(k)*c(n-k)).
%C A172350 Row sums are 1, 2, 3, 14, 90, 986, 15282, 453308, 22013694, 1746038420, 222562828116,...
%e A172350 1;
%e A172350 1, 1;
%e A172350 1, 1, 1;
%e A172350 1, 6, 6, 1;
%e A172350 1, 11, 66, 11, 1;
%e A172350 1, 41, 451, 451, 41, 1;
%e A172350 1, 96, 3936, 7216, 3936, 96, 1;
%e A172350 1, 301, 28896, 197456, 197456, 28896, 301, 1;
%e A172350 1, 781, 235081, 3761296, 14019376, 3761296, 235081, 781, 1;
%e A172350 1, 2286, 1785366, 89565861, 781665696, 781665696, 89565861, 1785366, 2286, 1;
%e A172350 1, 6191, 14152626, 1842200151, 50409295041, 118031520096, 50409295041, 1842200151, 14152626, 6191, 1;
%t A172350 Clear[f, c, a, t];
%t A172350 f[0, a_] := 0; f[1, a_] := 1;
%t A172350 f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];
%t A172350 c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
%t A172350 t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
%t A172350 Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
%t A172350 Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
%Y A172350 Cf. A010048 (m=1), A015109 (m=2), A172349 (m=4), A172351 (m=6).
%K A172350 nonn,tabl
%O A172350 0,8
%A A172350 _Roger L. Bagula_ and _Gary W. Adamson_, Feb 01 2010