A296436 Expansion of e.g.f. log(1 + arcsin(x))*exp(x).

0, 1, 1, 3, 0, 28, -85, 1029, -6440, 79136, -724305, 9982005, -118974856, 1858582100, -27126378357, 478338929509, -8227405849840, 162502213354272, -3209170996757057, 70409595412300877, -1566861832498793248, 37885426233247176772, -936732798302547171509, 24780850678372964078189

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

E.g.f.: log(1 - i*log(i*x + sqrt(1 - x^2)))*exp(x), where i is the imaginary unit.

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

Example

E.g.f.: A(x) = x/1! + x^2/2! + 3*x^3/3! + 28*x^5/5! - 85*x^6/6! + 1029*x^7/7! - 6440*x^8/8! + ...

Maple

a:=series(log(1+arcsin(x))*exp(x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 23; CoefficientList[Series[Log[1 + ArcSin[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[1 - I Log[I x + Sqrt[1 - x^2]]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + asin(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017

Crossrefs

Cf. A009334, A009337, A009353, A189815, A291482, A296437.

Sequence in context: A238104 A143769 A190963 * A215588 A215683 A215586

Adjacent sequences: A296433 A296434 A296435 * A296437 A296438 A296439

Keyword

sign

Author

Ilya Gutkovskiy, Dec 12 2017

Status

approved