A173918 - OEIS

%I #2 Mar 30 2012 17:34:39

%S 1,1,1,1,4,1,1,28,28,1,1,133,931,133,1,1,760,25270,25270,760,1,1,3880,

%T 737200,3501700,737200,3880,1,1,21049,20417530,554190100,554190100,

%U 20417530,21049,1,1,110236,580089391,80383815610,459336089200

%N A double product sequence based on a=3;f(n,a)=f(n-1,a)+a*f(n-2,a)

%C Row sums are:

%C {1, 2, 6, 58, 1199, 52062, 4983862, 1149257360, 621264119676, 736123531927540,

%C 2029965262731727157,...}.

%C I get these same sequences using a Narayana form:

%C w[n_, m_, q_] := c[n - 1, q]*c[n, q]/(c[m - 1, q]*c[n - m, q]*c[m - 1, q]*c[n - m + 1, q]*f[m, q])

%F c(n,a)=If[n == 0, 1, Product[f(i, a)*f(i + 1, a), {i, 1, n}]]

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 28, 28, 1},

%e {1, 133, 931, 133, 1},

%e {1, 760, 25270, 25270, 760, 1},

%e {1, 3880, 737200, 3501700, 737200, 3880, 1},

%e {1, 21049, 20417530, 554190100, 554190100, 20417530, 21049, 1},

%e {1, 110236, 580089391, 80383815610, 459336089200, 80383815610, 580089391, 110236, 1},

%e {1, 588772, 16225967548, 12197871104209, 355847668303240, 355847668303240, 12197871104209, 16225967548, 588772, 1},

%e {1, 3109597, 457710911221, 1802007857477077, 285191454075451081, 1455977423437829203, 285191454075451081, 1802007857477077, 457710911221, 3109597, 1}

%t Clear[t, n, m, c, q, w, f, a];

%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]*f[i + 1, a], {i, 1, n}]];

%t w[n_, m_, q_] := c[n, q]/(c[m, q]*c[n - m, q]);

%t Table[Table[Table[w[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 12}];

%t Table[Flatten[Table[Table[w[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 12}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 02 2010