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 A009390 #34 Sep 08 2022 08:44:37
%S A009390 0,1,1,0,0,5,5,-56,-56,1329,1329,-49192,-49192,2653573,2653573,
%T A009390 -196707408,-196707408,19194804737,19194804737,-2385684870704,
%U A009390 -2385684870704,367985503366821,367985503366821,-68980888889771080,-68980888889771080
%N A009390 Expansion of e.g.f.: log(1 + tanh(x))*exp(x).
%H A009390 G. C. Greubel, <a href="/A009390/b009390.txt">Table of n, a(n) for n = 0..486</a>
%F A009390 G.f.: x/(x^2-1)*(T(0)*(1+x)/(1+2*x) -2), where T(k) = 1 - x^2*(k+1)^2/(x^2*(k+1)^2 + (1+2*x)^2/T(k+1)); (continued fraction). - _Sergei N. Gladkovskii_, Nov 11 2013
%F A009390 a(n) = Sum_{k=0..floor((n-1)/2)} A028296(k). - _Daniel Suteu_, Nov 16 2018
%F A009390 a(n) = Sum_{k=0..n-1} E(k), where E(k) = A122045(k). - _Amiram Eldar_ and _Thomas Ordowski_, Feb 06 2020
%p A009390 seq(add(euler(k), k=0..n-1), n=0..24); # _Peter Luschny_, Feb 06 2020
%t A009390 With[{nmax = 30}, CoefficientList[Series[Log[1 + Tanh[x]]*Exp[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Nov 16 2018 *)
%o A009390 (PARI) a(n) = sum(k=0, floor((n-1)/2), 2*imag(polylog(-2*k, I))); \\ _Daniel Suteu_, Nov 16 2018
%o A009390 (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(log(1+tanh(x))*exp(x)))) \\ _G. C. Greubel_, Nov 16 2018
%o A009390 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x)*Log(1 + Tanh(x)))); [0] cat [Factorial(n)*b[n]: n in [1..(m-1)]]; // _G. C. Greubel_, Nov 16 2018
%Y A009390 Cf. A122045, A173226.
%K A009390 sign,easy
%O A009390 0,6
%A A009390 _R. H. Hardin_
%E A009390 Extended with signs by _Olivier Gérard_, Mar 15 1997