OFFSET
1,1
COMMENTS
Row sums = primes.
Right border = A007442, (2, 1, 1, -1, 3, -9...), = inverse binomial transform of the primes.
FORMULA
p(x,n)=Sum[Prime[k + 1]*Binomial[n,k]*x^k*(1 - x)^(n - k), {k, 0, n}]; t(n,m)=coefficients(p(x,n)). - Roger L. Bagula and Gary W. Adamson, Oct 01 2008
EXAMPLE
Row 5: sum = 11 = p5 since (2 + 4 + 6 - 4 + 3) = 11.
Triangle begins:
{2},
{2, 1},
{2, 2, 1},
{2, 3, 3, -1},
{2, 4, 6, -4, 3},
{2, 5, 10, -10, 15, -9},
{2, 6, 15, -20, 45, -54, 23},
{2, 7, 21, -35, 105, -189, 161, -53},
{2, 8, 28, -56, 210, -504, 644, -424, 115},
{2, 9, 36, -84, 378, -1134, 1932, -1908, 1035, -237},
{2, 10, 45, -120, 630, -2268, 4830, -6360, 5175, -2370, 457}
...
MATHEMATICA
Clear[p, x, n, m]; Sum[Prime[k + 1]*Binomial[n, k]*x^k*(1 - x)^(n - k), {k, 0, n}]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}]; Flatten[%] - Roger L. Bagula and Gary W. Adamson, Oct 01 2008
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Nov 07 2006
EXTENSIONS
More terms from Roger L. Bagula and Gary W. Adamson, Oct 01 2008
STATUS
approved