A083008 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).

0, 1, -3, 3, 9, -25, -99, 427, 2193, -12465, -79515, 555731, 4247577, -35135945, -313193811, 2990414715, 30461046561, -329655706465, -3777604994187, 45692713833379, 581778811909545, -7777794952988025, -108933009112011843, 1595024111042171723, 24370176181315498929

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..485

Formula

E.g.f.: 4*x/(1+exp(x)+exp(2*x)+exp(3*x)). - Ira M. Gessel, Feb 23 2012

a(n) ~ n! * (cos(n*Pi/2)-sin(n*Pi/2)) * 2^(n+1) / Pi^n. - Vaclav Kotesovec, Mar 02 2014

Mathematica

Range[0, 15]! CoefficientList[ Series[ 4x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)
Table[Sum[4^k*BernoulliB[k] Binomial[n, k], {k, 0, n - 1}], {n, 0, 24}] (* Michael De Vlieger, Sep 28 2016 *)

Prog

(PARI) a(n)=sum(k=0, n-1, 4^k*binomial(n, k)*bernfrac(k))

Crossrefs

Cf. A001469.

Bisection is A009843.

Cf. A036968, A083007, A083009, A083010, A083011, A083012, A083013, A083014.

Sequence in context: A184694 A215885 A176158 * A268092 A229024 A117976

Adjacent sequences: A083005 A083006 A083007 * A083009 A083010 A083011

Keyword

sign

Author

Benoit Cloitre, May 31 2003

Extensions

Offset changed to 0 by Seiichi Manyama, Sep 28 2016

Status

approved