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A154096 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))]. 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are: 1, 2, 6, 24, 93, 274, 159, 876, 6307, 35498, 107218, ...

The beginning of the sequence is Eulerian numbers-like.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows

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

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

CROSSREFS

Cf. A154097.

Sequence in context: A287532 A112500 A152938 * A146898 A152970 A154986

Adjacent sequences:  A154093 A154094 A154095 * A154097 A154098 A154099

KEYWORD

nonn,tabl,frac

AUTHOR

Roger L. Bagula, Jan 04 2009

STATUS

approved

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Last modified February 21 06:40 EST 2019. Contains 320371 sequences. (Running on oeis4.)