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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,6,1,1,30,30,1,1,240,1200,240,1,1,1560,62400,62400,1560,1,1,
%T 10920,2839200,22713600,2839200,10920,1,1,74256,135145920,7027587840,
%U 7027587840,135145920,74256,1,1,510510,6318071760,2299778120640
%N A four product triangle sequence based on :a=1;f(n,a)=f(n - 1, a) + a*f(n - 2, a)
%C Row sums are:
%C {1, 2, 8, 62, 1682, 127922, 28413842, 14325616034, 19560751189982,
%C 68454330820638842, 661989975165467768162,...}
%F a=1;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, 6, 1},
%e {1, 30, 30, 1},
%e {1, 240, 1200, 240, 1},
%e {1, 1560, 62400, 62400, 1560, 1},
%e {1, 10920, 2839200, 22713600, 2839200, 10920, 1},
%e {1, 74256, 135145920, 7027587840, 7027587840, 135145920, 74256, 1},
%e {1, 510510, 6318071760, 2299778120640, 14948557784160, 2299778120640, 6318071760, 510510, 1},
%e {1, 3495030, 297374627550, 736061678111760, 33490806354085080, 33490806354085080, 736061678111760, 297374627550, 3495030, 1},
%e {1, 23965920, 13960268229600, 237561884463103200, 73501647052884130080, 514511529370188910560, 73501647052884130080, 237561884463103200, 13960268229600, 23965920, 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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