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A154096
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A rational based combinatorial 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)).
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0
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The row sums are:
{1, 2, 6, 24, 93, 274, 159, 876, 6307, 35498, 107218,...}.
The begining of the sequence is Eulerian numbers-like.
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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)).
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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}
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MATHEMATICA
| Clear[a, b, t, f]; 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[%]
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CROSSREFS
| Sequence in context: A087903 A112500 A152938 * A146898 A152970 A154986
Adjacent sequences: A154093 A154094 A154095 * A154097 A154098 A154099
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 04 2009
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