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%I #31 Sep 28 2016 08:55:54
%S 0,1,-3,3,9,-25,-99,427,2193,-12465,-79515,555731,4247577,-35135945,
%T -313193811,2990414715,30461046561,-329655706465,-3777604994187,
%U 45692713833379,581778811909545,-7777794952988025,-108933009112011843,1595024111042171723,24370176181315498929
%N a(n) = Sum_{k=0..n-1} 4^k*B(k)*C(n,k) where B(k) is the k-th Bernoulli number and C(n,k) = binomial(n,k).
%H Seiichi Manyama, <a href="/A083008/b083008.txt">Table of n, a(n) for n = 0..485</a>
%F E.g.f.: 4*x/(1+exp(x)+exp(2*x)+exp(3*x)). - _Ira M. Gessel_, Feb 23 2012
%F a(n) ~ n! * (cos(n*Pi/2)-sin(n*Pi/2)) * 2^(n+1) / Pi^n. - _Vaclav Kotesovec_, Mar 02 2014
%t Range[0, 15]! CoefficientList[ Series[ 4x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x]), {x, 0, 15}], x] (* _Robert G. Wilson v_, Oct 26 2012 *)
%t Table[Sum[4^k*BernoulliB[k] Binomial[n, k], {k, 0, n - 1}], {n, 0, 24}] (* _Michael De Vlieger_, Sep 28 2016 *)
%o (PARI) a(n)=sum(k=0,n-1,4^k*binomial(n,k)*bernfrac(k))
%Y Cf. A001469.
%Y Bisection is A009843.
%Y Cf. A036968, A083007, A083009, A083010, A083011, A083012, A083013, A083014.
%K sign
%O 0,3
%A _Benoit Cloitre_, May 31 2003
%E Offset changed to 0 by _Seiichi Manyama_, Sep 28 2016