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A154096
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))].
2
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, 1, 23, 23, 391, 391, 23, 23, 1, 1, 13, 299, 299, 5083, 299, 299, 13, 1, 1, 29, 377, 8671, 8671, 8671, 8671, 377, 29, 1, 1, 16, 58, 1508, 17342, 69368, 17342, 1508, 58, 16, 1
OFFSET
0,5
FORMULA
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))].
EXAMPLE
{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},
{1, 23, 23, 391, 391, 23, 23, 1},
{1, 13, 299, 299, 5083, 299, 299, 13, 1},
{1, 29, 377, 8671, 8671, 8671, 8671, 377, 29, 1},
{1, 16, 58, 1508, 17342, 69368, 17342, 1508, 58, 16, 1}.
MATHEMATICA
f[n_] = Product[Prime[a]*k + Prime[b], {k, 0, n}];
t[n_, m_] = FullSimplify[f[n]/(f[n - m]*f[m])];
a = 2; b = 1; Table[Table[Numerator[t[n, m]], {m, 0, n}], {n, 0, 10}]//Flatten
CROSSREFS
Cf. A154097.
Sequence in context: A287532 A112500 A152938 * A146898 A152970 A154986
KEYWORD
nonn,tabl,frac
AUTHOR
Roger L. Bagula, Jan 04 2009
STATUS
approved