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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
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, 4, 44, 44, 4, 10, 2, 2, 5, 40, 22, 308, 22, 40, 5, 2, 2, 10, 40, 440, 308, 308, 440, 40, 10, 2, 2, 5, 5, 55, 385, 1309, 385, 55, 5, 5, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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) = Denominator[f(n)/(f(n-m)*f(m))].

EXAMPLE

{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, 4, 44, 44, 4, 10, 2},

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

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

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

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[Denominator[t[n, m]], {m, 0, n}], {n, 0, 10}]//Flatten

CROSSREFS

Cf. A154096.

Sequence in context: A066180 A123487 A130325 * A221491 A224254 A107604

Adjacent sequences:  A154094 A154095 A154096 * A154098 A154099 A154100

KEYWORD

nonn,tabl,frac

AUTHOR

Roger L. Bagula, Jan 04 2009

STATUS

approved

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)