Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Sep 28 2016 09:54:34
%S 0,1,-4,6,16,-74,-264,1946,9056,-88434,-512024,6154786,42716496,
%T -607884394,-4920817384,80834386026,747784582336,-13923204233954,
%U -144898927180344,3015393801263666,34867899296006576,-801997872697905114,-10201104981227536904,256982712667627683706
%N a(n) = Sum_{k=0,n-1} 5^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number.
%H Seiichi Manyama, <a href="/A083009/b083009.txt">Table of n, a(n) for n = 0..467</a>
%F E.g.f.: 5x/(1+exp(x)+exp(2x)+exp(3x)+exp(4x)). - _Benoit Cloitre_, Oct 26 2012 (following I. Gessel).
%t 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 *)
%t Table[Sum[5^k*BernoulliB[k] Binomial[n, k], {k, 0, n - 1}], {n, 0, 23}] (* _Michael De Vlieger_, Sep 28 2016 *)
%o (PARI) a(n)=sum(k=0,n-1,5^k*binomial(n,k)*bernfrac(k))
%Y Cf. A001469.
%Y Cf. A036968, A083007, A083008, 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