A083009 a(n) = Sum_{k=0,n-1} 5^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number.

0, 1, -4, 6, 16, -74, -264, 1946, 9056, -88434, -512024, 6154786, 42716496, -607884394, -4920817384, 80834386026, 747784582336, -13923204233954, -144898927180344, 3015393801263666, 34867899296006576, -801997872697905114, -10201104981227536904, 256982712667627683706

Offset: 0

Author

Benoit Cloitre, May 31 2003

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..467

Crossrefs

Cf. A001469.

Cf. A036968, A083007, A083008, A083010, A083011, A083012, A083013, A083014.

Programs

Mathematica

Range[0, 15]! CoefficientList[ Series[ 5x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)
Table[Sum[5^k*BernoulliB[k] Binomial[n, k], {k, 0, n - 1}], {n, 0, 23}] (* Michael De Vlieger, Sep 28 2016 *)

PARI

a(n)=sum(k=0,n-1,5^k*binomial(n,k)*bernfrac(k))

Formula

E.g.f.: 5x/(1+exp(x)+exp(2x)+exp(3x)+exp(4x)). - Benoit Cloitre, Oct 26 2012 (following I. Gessel).

Extensions

Offset changed to 0 by Seiichi Manyama, Sep 28 2016