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 A154097 A rational based combinatorial triangular sequence: f(n) = Product[Prime[a]*k + Prime[b],{k,0,n}]; a = 2; b = 1; t(n,m) = Denominator[f(n)/(f(n-m)*f(m))]. 2

%I

%S 2,2,2,2,5,2,2,10,10,2,2,5,40,5,2,2,10,40,40,10,2,2,1,4,22,4,1,2,2,10,

%T 4,44,44,4,10,2,2,5,40,22,308,22,40,5,2,2,10,40,440,308,308,440,40,10,

%U 2,2,5,5,55,385,1309,385,55,5,5,2

%N A rational based combinatorial triangular sequence: f(n) = Product[Prime[a]*k + Prime[b],{k,0,n}]; a = 2; b = 1; t(n,m) = Denominator[f(n)/(f(n-m)*f(m))].

%C The row sums are: {2, 4, 9, 24, 54, 104, 36, 120, 446, 1600, 2213,...}.

%H G. C. Greubel, <a href="/A154097/b154097.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) = Denominator[f(n)/(f(n-m)*f(m))].

%e {2},

%e {2, 2},

%e {2, 5, 2},

%e {2, 10, 10, 2},

%e {2, 5, 40, 5, 2},

%e {2, 10, 40, 40, 10, 2},

%e {2, 1, 4, 22, 4, 1, 2},

%e {2, 10, 4, 44, 44, 4, 10, 2},

%e {2, 5, 40, 22, 308, 22, 40, 5, 2},

%e {2, 10, 40, 440, 308, 308, 440, 40, 10, 2},

%e {2, 5, 5, 55, 385, 1309, 385, 55, 5, 5, 2}

%t Clear[a, b, t, f]; 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[Denominator[t[n, m]], {m, 0, n}], {n, 0, 10}]//Flatten

%Y Cf. A154096.

%K nonn,tabl,frac

%O 0,1

%A _Roger L. Bagula_, Jan 04 2009

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Last modified June 5 15:20 EDT 2020. Contains 334850 sequences. (Running on oeis4.)