A012277 Expansion of e.g.f. arcsinh(exp(x)*log(x+1)).

0, 1, 1, 1, -6, -17, -35, 901, 4284, 4201, -614267, -4098107, 8297630, 1150691631, 9449070657, -66322881767, -4588041616648, -41917690024495, 618354247728873, 33330584633391337, 310446365545119298

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..438

Example

arcsinh(exp(x)*log(x+1)) = x+1/2!*x^2+1/3!*x^3-6/4!*x^4-17/5!*x^5 ...

Maple

seq(coeff(series(factorial(n)*arcsinh(exp(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 28 2018

Mathematica

Range[0, 20]! CoefficientList[ Series[ ArcSinh[ Exp[x] Log[x + 1]], {x, 0, 20}], x] (* Robert G. Wilson v, Feb 22 2013 *)

Prog

(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(asinh(exp(x)* log(x+1))))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(Exp(x)*Log(x+1)) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018

Crossrefs

Sequence in context: A023545 A038633 A083045 * A358245 A307502 A084990

Adjacent sequences: A012274 A012275 A012276 * A012278 A012279 A012280

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Corrected the offset, Robert G. Wilson v, Feb 22 2013

Status

approved