A172351 - OEIS

%I #4 Jul 05 2012 11:46:37

%S 1,1,1,1,1,1,1,7,7,1,1,13,91,13,1,1,55,715,715,55,1,1,133,7315,13585,

%T 7315,133,1,1,463,61579,483835,483835,61579,463,1,1,1261,583843,

%U 11093017,46931995,11093017,583843,1261,1,1,4039,5093179,336877411

%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=6.

%C Start from the generalized Fibonacci sequence A015441 and its partial products c(n) = 1, 1, 1, 7, 91, 5005, 665665, 308202895, 388643850595, 1569732512553205... Then t(n,k) = c(n)/(c(k)*c(n-k)).

%C Row sums are 1, 2, 3, 16, 119, 1542, 28483, 1091756, 70288239, 7576979362, 1345651717403,..

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 7, 7, 1;

%e 1, 13, 91, 13, 1;

%e 1, 55, 715, 715, 55, 1;

%e 1, 133, 7315, 13585, 7315, 133, 1;

%e 1, 463, 61579, 483835, 483835, 61579, 463, 1;

%e 1, 1261, 583843, 11093017, 46931995, 11093017, 583843, 1261, 1;

%e 1, 4039, 5093179, 336877411, 3446515051, 3446515051, 336877411, 5093179, 4039, 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), A172350 (m=5), A172352 (m=7).

%K nonn,tabl

%O 0,8

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