cp's OEIS Frontend

A172353 Triangle t(n,k) of Padovan factorial ratios c(n)/(c(k)*c(n-k)) where c(n) = A126772(n).

%I A172353 #5 Jul 05 2012 12:06:32
%S A172353 1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,1,2,4,4,2,1,1,3,6,12,6,3,1,1,4,12,24,
%T A172353 24,12,4,1,1,5,20,60,60,60,20,5,1,1,7,35,140,210,210,140,35,7,1,1,9,
%U A172353 63,315,630,945,630,315,63,9,1
%N A172353 Triangle t(n,k) of Padovan factorial ratios c(n)/(c(k)*c(n-k)) where c(n) = A126772(n).
%C A172353 Start from the Padovan sequence A134816 and its partial products A126772, extended by A126772(0)=1. Then t(n,k) = c(n)/(c(k)*c(n-k)).
%C A172353 Row sums are 1, 2, 3, 4, 8, 14, 32, 82, 232, 786, 2981,..
%e A172353 1;
%e A172353 1, 1;
%e A172353 1, 1, 1;
%e A172353 1, 1, 1, 1;
%e A172353 1, 2, 2, 2, 1;
%e A172353 1, 2, 4, 4, 2, 1;
%e A172353 1, 3, 6, 12, 6, 3, 1;
%e A172353 1, 4, 12, 24, 24, 12, 4, 1;
%e A172353 1, 5, 20, 60, 60, 60, 20, 5, 1;
%e A172353 1, 7, 35, 140, 210, 210, 140, 35, 7, 1;
%e A172353 1, 9, 63, 315, 630, 945, 630, 315, 63, 9, 1;
%t A172353 Clear[f, c, a, t];
%t A172353 f[0, a_] := 0; f[1, a_] := 1; f[2, a_] := 1;
%t A172353 f[n_, a_] := f[n, a] = a*f[n - 2, a] + f[n - 3, a];
%t A172353 c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
%t A172353 t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
%t A172353 Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
%t A172353 Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
%Y A172353 Cf. A010048, A172355
%K A172353 nonn,tabl
%O A172353 0,12
%A A172353 _Roger L. Bagula_, Feb 01 2010