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A297210
Expansion of e.g.f. log(1 + arcsinh(x))*exp(-x).
3
0, 1, -3, 7, -16, 48, -213, 1027, -4856, 32512, -309377, 2527963, -16805072, 179877332, -2916171997, 32511289795, -227822369168, 3575741575680, -98643332014049, 1352701143217491, -6534261348983096, 168508582018012980, -9094443640555413357, 143341194607564099595
OFFSET
0,3
EXAMPLE
log(1 + arcsinh(x))*exp(-x) = x/1! - 3*x^2/2! + 7*x^3/3! - 16*x^4/4! + 48*x^5/5! - 213*x^6/6! + ...
MAPLE
a:=series(log(1+arcsinh(x))*exp(-x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[1 + ArcSinh[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 27 2017
STATUS
approved