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, 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

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: A123487 A130325 A362034 * A221491 A224254 A107604

Adjacent sequences: A154094 A154095 A154096 * A154098 A154099 A154100

Keyword

nonn,tabl,frac

Author

Roger L. Bagula, Jan 04 2009

Status

approved