A213615 Triangle read by rows, coefficients of the Bernoulli polynomials B_{n}(x) times A144845(n) in descending order of powers.

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

Links

T. D. Noe, Rows n = 0..100 of triangle, flattened

Peter Luschny, The Computation and Asymptotics of the Bernoulli numbers.

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

Cf. A053383, A144845, A213616.

Sequence in context: A374625 A218853 A048998 * A049019 A133314 A208909

Adjacent sequences: A213612 A213613 A213614 * A213616 A213617 A213618

Keyword

sign,tabl

Author

Peter Luschny, Jun 16 2012

Status

approved