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%I #21 Sep 28 2016 09:55:21
%S 0,1,-5,10,25,-170,-575,6370,28225,-415826,-2294975,41649850,
%T 275622625,-5922729722,-45718037855,1134081384850,10004182986625,
%U -281284596509858,-2791456543622015,87722769712529770,967282878165054625,-33597252908389628234,-407509096583935700255
%N a(n) = 6^n(B_n(1/6)-B_n(0)) where B_n(x) is the n-th Bernoulli polynomial.
%H Seiichi Manyama, <a href="/A083010/b083010.txt">Table of n, a(n) for n = 0..452</a>
%F E.g.f.: 6x(exp(x)-1)/(exp(6x)-1). - _Michael Somos_, Aug 02 2006
%F a(n) = Sum_{k=0..n-1} 6^k*B(k)*C(n,k) where B(k) is the k-th Bernoulli number and C(n,k) = binomial(n,k).
%t Range[0, 15]! CoefficientList[ Series[ 6x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x] + Exp[ 5x]), {x, 0, 15}], x] (* _Robert G. Wilson v_, Oct 26 2012 *)
%o (PARI) a(n)=sum(k=0,n-1,6^k*binomial(n,k)*bernfrac(k))
%o (PARI) {a(n)=if(n<1, 0, n!*polcoeff( 6*x*(exp(x+x*O(x^n))-1)/(exp(6*x +x*O(x^n))-1), n))} /* _Michael Somos_, Aug 02 2006 */
%Y Cf. A001469.
%Y Cf. A036968, A083007, A083008, A083009, A083011, A083012, A083013, A083014.
%K sign
%O 0,3
%A _Benoit Cloitre_, May 31 2003