login
A213615
Triangle read by rows, coefficients of the Bernoulli polynomials B_{n}(x) times A144845(n) in descending order of powers.
3
1, 2, -1, 6, -6, 1, 2, -3, 1, 0, 30, -60, 30, 0, -1, 6, -15, 10, 0, -1, 0, 42, -126, 105, 0, -21, 0, 1, 6, -21, 21, 0, -7, 0, 1, 0, 30, -120, 140, 0, -70, 0, 20, 0, -1, 10, -45, 60, 0, -42, 0, 20, 0, -3, 0, 66, -330, 495, 0, -462, 0, 330, 0, -99, 0, 5, 6, -33
OFFSET
0,2
FORMULA
T(n,k) = A144845(n)*[x^(n-k)]B{n}(x).
EXAMPLE
b(0,x) = 1
b(1,x) = 2*x - 1
b(2,x) = 6*x^2 - 6*x + 1
b(3,x) = 2*x^3 - 3*x^2 + x
b(4,x) = 30*x^4 - 60*x^3 + 30*x^2 - 1
b(5,x) = 6*x^5 - 15*x^4 + 10*x^3 - x
MAPLE
seq(seq(coeff(denom(bernoulli(i, x))*bernoulli(i, x), x, i-j), j=0..i), i=0..12);
MATHEMATICA
Flatten[Table[p = Reverse[CoefficientList[BernoulliB[n, x], x]]; (LCM @@ Denominator[p])*p, {n, 0, 10}]] (* T. D. Noe, Nov 07 2012 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Jun 16 2012
STATUS
approved