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 A296437 #13 Mar 27 2019 10:04:03
%S A296437 0,1,1,1,0,8,-5,-51,-504,8224,-12865,-296155,-2166736,73348780,
%T A296437 -116217309,-7440979651,-39733320080,2564082122752,-3056854891489,
%U A296437 -544155777899859,-2138400746459448,251904027415707852,-163714875656114029,-92626483427571793931,-273784346863222483272
%N A296437 Expansion of e.g.f. log(1 + arcsinh(x))*exp(x).
%H A296437 Andrew Howroyd, <a href="/A296437/b296437.txt">Table of n, a(n) for n = 0..200</a>
%H A296437 Vaclav Kotesovec, <a href="/A296437/a296437.jpg">Graph - The asymptotic ratio</a>
%F A296437 E.g.f.: log(1 + log(x + sqrt(1 + x^2)))*exp(x).
%F A296437 a(n) ~ n! * 2*sqrt(2/Pi) * (Pi*c - 2*s) / (n^(3/2) * (4 + Pi^2)) * (1 + (c*(-192 + 208*Pi - 96*Pi^2 - 8*Pi^3 - 12*Pi^4 + Pi^5) - 2*s*(80 + 48*Pi - 40*Pi^2 + 24*Pi^3 + Pi^4 + 3*Pi^5)) / (4*(4 + Pi^2)^2 * (c*Pi - 2*s)*n)), where s = sin(1 - Pi*n/2) and c = cos(1 - Pi*n/2). - _Vaclav Kotesovec_, Dec 21 2017
%e A296437 E.g.f.: A(x) = x/1! + x^2/2! + x^3/3! + 8*x^5/5! - 5*x^6/6! - 51*x^7/7! - 504*x^8/8! + ...
%p A296437 a:=series(log(1+arcsinh(x))*exp(x),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # _Paolo P. Lava_, Mar 27 2019
%t A296437 nmax = 24; CoefficientList[Series[Log[1 + ArcSinh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
%t A296437 nmax = 24; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
%o A296437 (PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + asinh(x + ox)) * exp(x + ox)))) \\ _Andrew Howroyd_, Dec 12 2017
%Y A296437 Cf. A009334, A009353, A009356, A291483, A296435, A296436.
%K A296437 sign
%O A296437 0,6
%A A296437 _Ilya Gutkovskiy_, Dec 12 2017