OFFSET
1,2
FORMULA
p(x,0) = 1. p(x,1) = 137-x. p(x,n) = (-1)^(n-1)*(137-n) + (-1)^(n-1)*137*x^(n-1) - (-1)^(n-1)*x^n for n > 1.
T(n,k) = [x^k] p(x,n).
EXAMPLE
p(x,134) = -3 - 137*x^133 + x^134.
Triangular sequence:
{1},
{137, -1},
{-135, -137, 1},
{134, 0, 137, -1},
{-133, 0, 0, -137, 1},
{132, 0, 0, 0, 137, -1},
{-131, 0, 0, 0, 0, -137, 1},
{130, 0, 0, 0, 0, 0, 137, -1},
...
MATHEMATICA
p[x_, n_] = (-1)^(n - 1)*(137 - n) + (-1)^(n - 1)*137*x^(n - 1) - (-1)^( n - 1)*x^n
a = Join[{1, 137 - x}, Table[p[x, n], {n, 2, 10}]]
c = Table[CoefficientList[a[[n]], x], {n, 1, Length[a]}]
Flatten[c]
PROG
(PARI) p(x, n) = if(n==0, 1, if(n==1, 137-x, (-1)^(n-1)*(137-n) + (-1)^(n-1)*137*x^(n-1) - (-1)^(n-1)*x^n))
T(n, k) = polcoef(p(x, n), k) \\ Jason Yuen, Jan 28 2025
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Jan 29 2008
EXTENSIONS
More terms from Jason Yuen, Jan 28 2025
STATUS
approved