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A172346
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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=8.
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1
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1, 1, 1, 1, 8, 1, 1, 65, 65, 1, 1, 528, 4290, 528, 1, 1, 4289, 283074, 283074, 4289, 1, 1, 34840, 18678595, 151727664, 18678595, 34840, 1, 1, 283009, 1232504195, 81326315267, 81326315267, 1232504195, 283009, 1, 1, 2298912, 81326598276
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OFFSET
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0,5
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COMMENTS
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Start from the generalized Fibonacci sequence A041025 and its partial products c(n) = 1, 1, 8, 520, 274560, 1177587840, 41027160345600,... Then t(n,k) = c(n)/(c(k)*c(n-k)).
Row sums are 1, 2, 10, 132, 5348, 574728, 189154536, 165118204944, 441439547818768, 3130197658239760416, 67978275921898969849504,...
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LINKS
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EXAMPLE
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1;
1, 1;
1, 8, 1;
1, 65, 65, 1;
1, 528, 4290, 528, 1;
1, 4289, 283074, 283074, 4289, 1;
1, 34840, 18678595, 151727664, 18678595, 34840, 1;
1, 283009, 1232504195, 81326315267, 81326315267, 1232504195, 283009, 1;
1, 2298912, 81326598276, 43591056675936, 354094776672518, 43591056675936, 81326598276, 2298912, 1;
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MATHEMATICA
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Clear[f, c, a, t];
f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 2, a];
c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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