A296727 Expansion of e.g.f. arcsinh(x)/(1 - x).

0, 1, 2, 5, 20, 109, 654, 4353, 34824, 324441, 3244410, 34795485, 417545820, 5536151685, 77506123590, 1144330385625, 18309286170000, 315366695240625, 5676600514331250, 106667957800963125, 2133359156019262500, 45229212438054868125, 995042673637207098750, 22696937952367956440625

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

E.g.f.: log(x + sqrt(1 + x^2))/(1 - x).

a(n) ~ n! * log(1 + sqrt(2)). - Vaclav Kotesovec, Dec 20 2017

Example

arcsinh(x)/(1 - x) = x/1! + 2*x^2/2! + 5*x^3/3! + 20*x^4/4! + 109*x^5/5! + ...

Maple

a:=series(arcsinh(x)/(1 - x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 23; CoefficientList[Series[ArcSinh[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[x + Sqrt[1 + x^2]]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) first(n) = x='x+O('x^n); Vec(serlaplace(asinh(x)/(1 - x)), -n) \\ Iain Fox, Dec 19 2017

Crossrefs

Cf. A001818, A009628, A081358, A186763, A281964, A296726.

Sequence in context: A152562 A006867 A170946 * A201224 A305922 A019536

Adjacent sequences: A296724 A296725 A296726 * A296728 A296729 A296730

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 19 2017

Status

approved