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 #14 Oct 02 2021 07:58:04
%S 0,1,2,2,-8,-76,-264,1672,36800,261648,-1443680,-66164704,-792152448,
%T 2482671424,289529373056,5294082629760,1648955815936,
%U -2474170098704128,-65494141255724544,-303927676523118080,35926135133071923200,1341060635191667045376
%N Expansion of e.g.f. arcsinh(x*exp(x)).
%H Seiichi Manyama, <a href="/A297010/b297010.txt">Table of n, a(n) for n = 0..100</a>
%e arcsinh(x*exp(x)) = x^1/1! + 2*x^2/2! + 2*x^3/3! - 8*x^4/4! - 76*x^5/5! - 264*x^6/6! + ...
%p a:=series(arcsinh(x*exp(x)),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 21; CoefficientList[Series[ArcSinh[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 21; CoefficientList[Series[Log[x Exp[x] + Sqrt[1 + x^2 Exp[2 x]]], {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) first(n) = my(x='x+O('x^n)); Vec(serlaplace(asinh(exp(x)*x)), -n) \\ _Iain Fox_, Dec 23 2017
%Y Cf. A001818, A009017, A009121, A009448, A009565, A009635, A009768, A191719, A216401, A297009.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Dec 23 2017