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

%I A213615 #11 Nov 07 2012 18:10:13
%S A213615 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,
%T A213615 -21,0,1,6,-21,21,0,-7,0,1,0,30,-120,140,0,-70,0,20,0,-1,10,-45,60,0,
%U A213615 -42,0,20,0,-3,0,66,-330,495,0,-462,0,330,0,-99,0,5,6,-33
%N A213615 Triangle read by rows, coefficients of the Bernoulli polynomials B_{n}(x) times A144845(n) in descending order of powers.
%H A213615 T. D. Noe, <a href="/A213615/b213615.txt">Rows n = 0..100 of triangle, flattened</a>
%H A213615 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/ComputationAndAsymptoticsOfBernoulliNumbers">The Computation and Asymptotics of the Bernoulli numbers.</a>
%F A213615 T(n,k) = A144845(n)*[x^(n-k)]B{n}(x).
%e A213615 b(0,x) =  1
%e A213615 b(1,x) =  2*x    -  1
%e A213615 b(2,x) =  6*x^2  -  6*x    + 1
%e A213615 b(3,x) =  2*x^3  -  3*x^2  + x
%e A213615 b(4,x) = 30*x^4  - 60*x^3  + 30*x^2  - 1
%e A213615 b(5,x) =  6*x^5  - 15*x^4  + 10*x^3  - x
%p A213615 seq(seq(coeff(denom(bernoulli(i,x))*bernoulli(i,x),x,i-j),j=0..i),i=0..12);
%t A213615 Flatten[Table[p = Reverse[CoefficientList[BernoulliB[n, x], x]]; (LCM @@ Denominator[p])*p, {n, 0, 10}]] (* _T. D. Noe_, Nov 07 2012 *)
%Y A213615 Cf. A053383, A144845, A213616.
%K A213615 sign,tabl
%O A213615 0,2
%A A213615 _Peter Luschny_, Jun 16 2012