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%I #13 Sep 27 2013 06:11:58
%S 1,2,-3,6,-18,13,2,-9,13,-6,30,-180,390,-360,119,6,-45,130,-180,119,
%T -30,42,-378,1365,-2520,2499,-1260,253,6,-63,273,-630,833,-630,253,
%U -42,30,-360,1820,-5040,8330,-8400,5060,-1680,239,10,-135,780,-2520,4998,-6300
%N Triangle read by rows, coefficients of the Bernoulli nabla polynomials BN_{n}(x) times A144845(n) in descending order of powers.
%C The polynomials BN_{n}(x) have the e.g.f. t*exp(t*(x-1))/(exp(t)-1). The adjunct 'nabla' in the name refers to the backward difference operation.
%C BN_{n}(1) are the Bernoulli numbers.
%C In the difference table of the Bernoulli polynomials the polynomials BN_{n}(x) appear as the top row (see the link).
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/ComputationAndAsymptoticsOfBernoulliNumbers">The Computation and Asymptotics of the Bernoulli numbers.</a>
%F T(n,k) = A144845(n)*[x^(n-k)]BN{n}(x).
%e bn(0,x) = 1,
%e bn(1,x) = 2*x - 3,
%e bn(2,x) = 6*x^2 - 18*x + 13,
%e bn(3,x) = 2*x^3 - 9*x^2 + 13*x - 6,
%e bn(4,x) = 30*x^4 - 180*x^3 + 390*x^2 - 360*x + 119,
%e bn(5,x) = 6*x^5 - 45*x^4 + 130*x^3 - 180*x^2 + 119*x - 30.
%p seq(seq(coeff(denom(bernoulli(i, x))*bernoulli(i, x - 1), x, i - j), j=0..i), i=0..12);
%t Table[If[i == 0, 1, 1/First[ FactorTerms[ BernoulliB[i, x]]]]*Table[ Coefficient[ Denominator[ BernoulliB[i, x]]*BernoulliB[i, x-1], x, i-j], {j, 0, i}], {i, 0, 12}] // Flatten (* _Jean-François Alcover_, Sep 27 2013, after Maple *)
%Y A053383, A144845, A213615.
%K sign,tabl
%O 0,2
%A _Peter Luschny_, Jun 16 2012
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