A291483 Expansion of e.g.f. arcsinh(x)*exp(x).

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

Links

Table of n, a(n) for n=0..25.

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

Cf. A001818, A009545, A012584, A131577, A291482.

Sequence in context: A151868 A344913 A052079 * A181295 A166299 A182508

Adjacent sequences: A291480 A291481 A291482 * A291484 A291485 A291486

Keyword

sign

Author

Ilya Gutkovskiy, Aug 24 2017

Status

approved