A296435 Expansion of e.g.f. log(1 + arcsinh(x)).

0, 1, -1, 1, -2, 13, -64, 173, -720, 12409, -114816, 370137, -1491456, 88556037, -1263184896, 2668274373, 21448022016, 2491377242481, -50233550831616, -34526890553679, 5153298175033344, 202383113207336829, -5453228045913292800, -25792743610973373219, 1393299559788718325760

Offset

0,5

Links

Robert Israel, Table of n, a(n) for n = 0..451

Formula

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

a(n) ~ 4*(Pi*cos(Pi*n/2) + 2*sin(Pi*n/2)) * n^(n-1) / ((4 + Pi^2) * exp(n)). - Vaclav Kotesovec, Dec 21 2017

Example

E.g.f.: A(x) = x/1! - x^2/2! + x^3/3! - 2*x^4/4! + 13*x^5/5! - 64*x^6/6! + ...

Maple

S:= series(ln(1+arcsinh(x)), x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Dec 12 2017

Mathematica

nmax = 24; CoefficientList[Series[Log[1 + ArcSinh[x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) Vecrev(Pol(serlaplace(log(1 + asinh(x + O(x^30)))))) \\ Andrew Howroyd, Dec 12 2017

Crossrefs

Cf. A001818, A003704, A110708, A189815, A202139, A296437.

Sequence in context: A089130 A081340 A211067 * A127531 A266633 A037745

Adjacent sequences: A296432 A296433 A296434 * A296436 A296437 A296438

Keyword

sign

Author

Ilya Gutkovskiy, Dec 12 2017

Status

approved