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A172345 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=7.

%I A172345 #5 Jul 05 2012 11:38:28
%S A172345 1,1,1,1,7,1,1,50,50,1,1,357,2550,357,1,1,2549,129999,129999,2549,1,1,
%T A172345 18200,6627400,47319636,6627400,18200,1,1,129949,337867400,
%U A172345 17224480052,17224480052,337867400,129949,1,1,927843,17224610001,6269758040364
%N A172345 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=7.
%C A172345 Start from the generalized Fibonacci sequence A054413 and its partial products c(n) = 1, 1, 7, 350, 124950, 318497550, 5796655410000,... Then t(n,k) = c(n)/(c(k)*c(n-k)).
%C A172345 Row sums are 1, 2, 9, 102, 3266, 265098, 60610838, 35124954804, 57340390811566,
%C A172345 237262009585104396, 2765506241462282647452,...}
%e A172345 1;
%e A172345 1, 1;
%e A172345 1, 7, 1;
%e A172345 1, 50, 50, 1;
%e A172345 1, 357, 2550, 357, 1;
%e A172345 1, 2549, 129999, 129999, 2549, 1;
%e A172345 1, 18200, 6627400, 47319636, 6627400, 18200, 1;
%e A172345 1, 129949, 337867400, 17224480052, 17224480052, 337867400, 129949, 1;
%e A172345 1, 927843, 17224610001, 6269758040364, 44766423655148, 6269758040364, 17224610001, 927843, 1;
%t A172345 Clear[f, c, a, t];
%t A172345 f[0, a_] := 0; f[1, a_] := 1;
%t A172345 f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 2, a];
%t A172345 c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
%t A172345 t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
%t A172345 Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
%t A172345 Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
%Y A172345 Cf. A010048 (m=1), A099927 (m=2), A172343 (m=6), A172346 (m=8).
%K A172345 nonn,tabl
%O A172345 0,5
%A A172345 _Roger L. Bagula_, Feb 01 2010