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A172346 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=8.

%I A172346 #5 Jul 05 2012 11:38:33
%S A172346 1,1,1,1,8,1,1,65,65,1,1,528,4290,528,1,1,4289,283074,283074,4289,1,1,
%T A172346 34840,18678595,151727664,18678595,34840,1,1,283009,1232504195,
%U A172346 81326315267,81326315267,1232504195,283009,1,1,2298912,81326598276
%N A172346 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=8.
%C A172346 Start from the generalized Fibonacci sequence A041025 and its partial products c(n) = 1, 1, 8, 520, 274560, 1177587840, 41027160345600,... Then t(n,k) = c(n)/(c(k)*c(n-k)).
%C A172346 Row sums are 1, 2, 10, 132, 5348, 574728, 189154536, 165118204944, 441439547818768, 3130197658239760416, 67978275921898969849504,...
%e A172346 1;
%e A172346 1, 1;
%e A172346 1, 8, 1;
%e A172346 1, 65, 65, 1;
%e A172346 1, 528, 4290, 528, 1;
%e A172346 1, 4289, 283074, 283074, 4289, 1;
%e A172346 1, 34840, 18678595, 151727664, 18678595, 34840, 1;
%e A172346 1, 283009, 1232504195, 81326315267, 81326315267, 1232504195, 283009, 1;
%e A172346 1, 2298912, 81326598276, 43591056675936, 354094776672518, 43591056675936, 81326598276, 2298912, 1;
%t A172346 Clear[f, c, a, t];
%t A172346 f[0, a_] := 0; f[1, a_] := 1;
%t A172346 f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 2, a];
%t A172346 c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
%t A172346 t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
%t A172346 Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
%t A172346 Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
%Y A172346 Cf. A010048 (m=1), A099927 (m=2), A172345 (m=7).
%K A172346 nonn,tabl
%O A172346 0,5
%A A172346 _Roger L. Bagula_, Feb 01 2010