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%I #11 Jun 03 2023 06:19:57
%S 1,1,1,1,4,1,1,11,11,1,1,7,77,7,1,1,17,119,119,17,1,1,2,17,119,17,2,1,
%T 1,23,23,391,391,23,23,1,1,13,299,299,5083,299,299,13,1,1,29,377,8671,
%U 8671,8671,8671,377,29,1,1,16,58,1508,17342,69368,17342,1508,58,16,1
%N Triangular sequence: f(n) = Product[Prime[a]*k + Prime[b], {k,0,n}]; a = 2; b = 1; t(n,m) = Numerator[f(n)/(f(n-m)*f(m))].
%H G. C. Greubel, <a href="/A154096/b154096.txt">Table of n, a(n) for the first 50 rows</a>
%F f(n) = Product[Prime[a]*k + Prime[b], {k,0,n}]; a = 2; b = 1; t(n,m) = Numerator[f(n)/(f(n-m)*f(m))].
%e {1},
%e {1, 1},
%e {1, 4, 1},
%e {1, 11, 11, 1},
%e {1, 7, 77, 7, 1},
%e {1, 17, 119, 119, 17, 1},
%e {1, 2, 17, 119, 17, 2, 1},
%e {1, 23, 23, 391, 391, 23, 23, 1},
%e {1, 13, 299, 299, 5083, 299, 299, 13, 1},
%e {1, 29, 377, 8671, 8671, 8671, 8671, 377, 29, 1},
%e {1, 16, 58, 1508, 17342, 69368, 17342, 1508, 58, 16, 1}.
%t f[n_] = Product[Prime[a]*k + Prime[b], {k, 0, n}];
%t t[n_, m_] = FullSimplify[f[n]/(f[n - m]*f[m])];
%t a = 2; b = 1; Table[Table[Numerator[t[n, m]], {m, 0, n}], {n, 0, 10}]//Flatten
%Y Cf. A154097.
%K nonn,tabl,frac
%O 0,5
%A _Roger L. Bagula_, Jan 04 2009
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