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A291483
Expansion of e.g.f. arcsinh(x)*exp(x).
2
0, 1, 2, 2, 0, 4, 40, -64, -1344, 3984, 85408, -356896, -8462080, 45908160, 1209040768, -8080805888, -235449260032, 1871655631104, 59955521585664, -552758145525248, -19339870285225984, 202927333558572032, 7707208199780517888, -90698934927786770432, -3718489569130941169664, 48507735629457304555520
OFFSET
0,3
FORMULA
E.g.f.: log(x + sqrt(1 + x^2))*exp(x).
EXAMPLE
E.g.f.: A(x) = x/1! + 2*x^2/2! + 2*x^3/3! + 4*x^5/5! + 40*x^6/6! - 64*x^7/7! - 1344*x^8/8! + ...
MAPLE
a:=series(arcsinh(x)*exp(x), x=0, 26): seq(n!*coeff(a, x, n), n=0..25); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 25; Range[0, nmax]! CoefficientList[Series[ArcSinh[x] Exp[x], {x, 0, nmax}], x]
nmax = 25; Range[0, nmax]! CoefficientList[Series[Log[x + Sqrt[1 + x^2]] Exp[x], {x, 0, nmax}], x]
nmax = 25; Range[0, nmax]! CoefficientList[Series[-Sum[((-1)^k (-1 + x + Sqrt[1 + x^2])^k)/k, {k, 1, Infinity}] Exp[x], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 24 2017
STATUS
approved