A296675 Expansion of e.g.f. 1/(1 - arcsinh(x)).

1, 1, 2, 5, 16, 69, 368, 2169, 14208, 109929, 970752, 8995821, 88341504, 988161069, 12276025344, 154843019169, 2009594658816, 29484826539345, 476778061430784, 7588488203093205, 121001549512310784, 2205431202369899925, 44538441694414110720, 852615914764223422665

Offset

0,3

Comments

a(48) is negative. - Vaclav Kotesovec, Jan 26 2020

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

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

a(n) ~ 8*((4 - Pi^2)*sin(Pi*n/2) - 4*Pi*cos(Pi*n/2)) * n^(n-1) / ((4 + Pi^2)^2 * exp(n)). - Vaclav Kotesovec, Dec 18 2017

Example

1/(1 - arcsinh(x)) = 1 + x/1! + 2*x^2/2! + 5*x^3/3! + 16*x^4/4! + 69*x^5/5! + ...

Maple

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

Mathematica

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

Prog

(PARI) x='x+O('x^99); Vec(serlaplace(1/(1-log(x+sqrt(1+x^2))))) \\ Altug Alkan, Dec 18 2017

Crossrefs

Cf. A000111, A001818, A006154, A189780.

Sequence in context: A107948 A220840 A058673 * A059295 A259408 A251684

Adjacent sequences: A296672 A296673 A296674 * A296676 A296677 A296678

Keyword

sign

Author

Ilya Gutkovskiy, Dec 18 2017

Status

approved