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A172343 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=6.

%I A172343 #5 Jul 05 2012 11:38:18
%S A172343 1,1,1,1,6,1,1,37,37,1,1,228,1406,228,1,1,1405,53390,53390,1405,1,1,
%T A172343 8658,2027415,12493260,2027415,8658,1,1,53353,76988379,2923477635,
%U A172343 2923477635,76988379,53353,1,1,328776,2923530988,684106251192
%N A172343 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=6.
%C A172343 Start from the generalized Fibonacci sequence A005668 and its partial products c(n) = 1, 1, 6, 222, 50616, 71115480, 615717825840, 32850393162041520... Then t(n,k) = c(n)/(c(k)*c(n-k)).
%C A172343 Row sums are 1, 2, 8, 76, 1864, 109592, 16565408, 6001038736, 5589714971584,
%C A172343 12478331908166432, 71624411004755875328,...
%e A172343 1;
%e A172343 1, 1;
%e A172343 1, 6, 1;
%e A172343 1, 37, 37, 1;
%e A172343 1, 228, 1406, 228, 1;
%e A172343 1, 1405, 53390, 53390, 1405, 1;
%e A172343 1, 8658, 2027415, 12493260, 2027415, 8658, 1;
%e A172343 1, 53353, 76988379, 2923477635, 2923477635, 76988379, 53353, 1;
%e A172343 1, 328776, 2923530988, 684106251192, 4215654749670, 684106251192, 2923530988, 328776, 1;
%t A172343 Clear[f, c, a, t];
%t A172343 f[0, a_] := 0; f[1, a_] := 1;
%t A172343 f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 2, a];
%t A172343 c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
%t A172343 t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
%t A172343 Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
%t A172343 Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
%Y A172343 Cf. A010048 (m=1), A099927 (m=2), A172342 (m=5), A172345 (m=7).
%K A172343 nonn,tabl
%O A172343 0,5
%A A172343 _Roger L. Bagula_, Feb 01 2010