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A174188 A four product triangle sequence based on :a=3;f(n,a)=f(n - 1, a) + a*f(n - 2, a) 0

%I

%S 1,1,1,1,28,1,1,532,532,1,1,21280,404320,21280,1,1,516040,392190400,

%T 392190400,516040,1,1,15997240,294829133200,11793165328000,

%U 294829133200,15997240,1,1,427715680,244366799454400,237035795470768000

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

%C Row sums are:

%C {1, 2, 30, 1066, 446882, 785412882, 12382855588882, 474560325395876162,

%C 149430618145736091033018, 183642180080454590264125715410,

%C 1840703499938423522875527863428804802,...}

%F a=3;f(n,a)=f(n - 1, a) + a*f(n - 2, a);

%F c(n,a)=If[n == 0 || n == 1, 1, Product[f(i - 1, a)*f(i, a)*f(i + 1, a)*f(i + 2, a), {i, 2, n}]];

%F t(n,m,a)=c(n,a)/(c(m,a)*c(n-m,a))

%e {1},

%e {1, 1},

%e {1, 28, 1},

%e {1, 532, 532, 1},

%e {1, 21280, 404320, 21280, 1},

%e {1, 516040, 392190400, 392190400, 516040, 1},

%e {1, 15997240, 294829133200, 11793165328000, 294829133200, 15997240, 1},

%e {1, 427715680, 244366799454400, 237035795470768000, 237035795470768000, 244366799454400, 427715680, 1},

%e {1, 12393061828, 189310959537323680, 5692580553287323057600, 138045078417217584146800, 5692580553287323057600, 189310959537323680, 12393061828, 1},

%e {1, 342789534892, 151721853568139975092, 121980856710070330416650080, 91699109031795370890716697640, 91699109031795370890716697640, 121980856710070330416650080, 151721853568139975092, 342789534892, 1},

%e {1, 9730799700160, 119129153690894980642240, 2775140915805593789011547872960, 55778725747162231920622684508253760, 1729140498162029189539303219755866560, 55778725747162231920622684508253760, 2775140915805593789011547872960, 119129153690894980642240, 9730799700160, 1}

%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 || n == 1, 1, Product[f[i - 1, a]*f[i, a]*f[i + 1, a]*f[i + 2, a], {i, 2, n}]];Q w[n_, m_, q_] := c[n, q]/(c[m, q]*c[n - m, q]);

%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 11 2010

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)