This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009362 #21 Apr 01 2017 14:06:35
%S A009362 0,1,-3,12,-66,480,-4368,47712,-608016,8855040,-145083648,2641216512,
%T A009362 -52891055616,1155444326400,-27344999497728,696933753434112,
%U A009362 -19031293222127616,554336947975618560,-17155693983744196608
%N A009362 Expansion of log(1 + sinh(x)/exp(x)).
%F A009362 a(n) = -Sum_{k>0} (-2*k)^n/3^k/k = -(-2)^n*polylog(-n+1, 1/3), n>0. - _Vladeta Jovovic_, Sep 30 2003
%F A009362 a(n) = -(-1)^n*Sum_{k=0..n-1} 3^k*Sum_{j=0..k} (-1)^j*(k-j)^n*C(n,j) for n>0. a(n) = -(-1)^n*Sum_{k=0..n-1} 3^k*A008292(n-1,k) for n>0, where A008292 are the Eulerian numbers. - _Paul D. Hanna_, Mar 29 2006
%F A009362 a(n) ~ (n-1)! * (-1)^(n+1) * (2/log(3))^n. - _Vaclav Kotesovec_, Jan 23 2015
%t A009362 Log[ 1+Sinh[ x ]/Exp[ x ] ]
%t A009362 CoefficientList[Series[Log[1 + Sinh[x]/E^x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)
%o A009362 (PARI) a(n)=-(-1)^n*sum(k=0,n-1,3^k*sum(j=0,k,(-1)^j*(k-j)^(n-1)*binomial(n,j))) \\ _Paul D. Hanna_, Mar 29 2006
%Y A009362 Cf. A008292 (Eulerian numbers).
%K A009362 sign,easy
%O A009362 0,3
%A A009362 _R. H. Hardin_
%E A009362 Extended with signs by _Olivier Gérard_, Mar 15 1997