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%I #7 May 23 2021 02:47:30
%S 1,1,1,1,2,1,1,3,3,1,1,2,7,2,1,1,3,3,3,3,1,1,6,9,20,9,6,1,1,7,21,35,
%T 35,21,7,1,1,8,28,56,70,56,28,8,1,1,5,36,84,126,126,84,36,5,1,1,10,25,
%U 120,210,252,210,120,25,10,1
%N See Mathematica program for definition.
%e {1},
%e {1, 1},
%e {1, 2, 1},
%e {1, 3, 3, 1},
%e {1, 2, 7, 2, 1},
%e {1, 3, 3, 3, 3, 1},
%e {1, 6, 9, 20, 9, 6, 1},
%e {1, 7, 21, 35, 35, 21, 7, 1},
%e {1, 8, 28, 56, 70, 56, 28, 8, 1},
%e {1, 5, 36, 84, 126, 126, 84, 36, 5, 1},
%e {1, 10, 25, 120, 210, 252, 210, 120, 25, 10, 1}
%t a[0] = 1;
%t a[n_] := a[n] = ((4*n - 2)/(n + 1))*a[n - 1];
%t b[0] = 1;
%t b[n_] := b[n] = If[IntegerQ[((3*n - 2)/(n + 1))*b[n - 1]], ((3*n - 2)/(n + 1))*b[n - 1], If[IntegerQ[((4*n - 2)/( n + 1))*b[n - 1]], ((4*n - 2)/(n + 1))*b[n - 1], n*b[n - 1]]];
%t c[0] = 1;
%t c[n_] := c[n] = If[IntegerQ[((6*n - 4)/(n + 1))*c[n - 1]], ((6*n - 4)/(n + 1))*c[n - 1], If[IntegerQ[((4*n - 2)/(n + 1))*c[n - 1]], ((4*n - 2)/(n + 1))*c[n - 1], n*c[n - 1]]];
%t t[n_, m_] := t[n, m] = If[IntegerQ[a[n]/(a[m]*a[n - m])], a[n]/(a[m]*a[n - m]), If[IntegerQ[b[ n]/(b[m]*b[n - m])], b[n]/(b[m]* b[n - m]), If[IntegerQ[ c[n]/(c[m]*c[n - m])], c[n]/(c[m]*c[n - m]), Binomial[n, m]]]];
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K nonn,uned
%O 0,5
%A _Roger L. Bagula_, Jan 24 2009
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