A172352 - OEIS

%I #4 Jul 05 2012 15:21:53

%S 1,1,1,1,1,1,1,8,8,1,1,15,120,15,1,1,71,1065,1065,71,1,1,176,12496,

%T 23430,12496,176,1,1,673,118448,1051226,1051226,118448,673,1,1,1905,

%U 1282065,28205430,133505702,28205430,1282065,1905,1,1,6616,12603480

%N 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 Start from the generalized Fibonacci sequence A015442 and its partial products c(n) = 1, 1, 1, 8, 120, 8520, 1499520, 1009176960, 1922482108800... Then t(n,k) = c(n)/(c(k)*c(n-k)).

%C Row sums are 1, 2, 3, 18, 152, 2274, 48776, 2340696, 192484504, 27026705688, 6379354108992,...

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 8, 8, 1;

%e 1, 15, 120, 15, 1;

%e 1, 71, 1065, 1065, 71, 1;

%e 1, 176, 12496, 23430, 12496, 176, 1;

%e 1, 673, 118448, 1051226, 1051226, 118448, 673, 1;

%e 1, 1905, 1282065, 28205430, 133505702, 28205430, 1282065, 1905, 1;

%e 1, 6616, 12603480, 1060267755, 12440474992, 12440474992, 1060267755, 12603480, 6616, 1;

%t Clear[f, c, a, t];

%t f[0, a_] := 0; f[1, a_] := 1;

%t f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];

%t c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];

%t t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);

%t Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];

%t Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]

%Y CF. A010048 (m=1), A015109 (m=2), A172351 (m=6).

%K nonn,tabl

%O 0,8

%A _Roger L. Bagula_ and _Gary W. Adamson_, Feb 01 2010