A013459 Expansion of e.g.f. exp(arctan(x) - log(x+1)).

1, 0, 1, -4, 9, -40, 385, -2700, 15505, -145360, 1886625, -19796500, 190881625, -2654379000, 44269902625, -625468889500, 8553276590625, -156119043652000, 3194978818578625, -57041478987070500

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..449

Formula

From Robert Israel, Jan 29 2018: (Start)

E.g.f.: exp(arctan(x) - log(x+1)).

(n+1)^2*(n+2)*a(n)+n*(n+2)*a(n+1)+(n+2)*a(n+2)+a(n+3) = 0. (End)

Maple

f:= gfun:-rectoproc({(n+1)^2*(n+2)*a(n)+n*(n+2)*a(n+1)+(n+2)*a(n+2)+a(n+3) = 0, a(0)=1, a(1)=0, a(2)=1}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Jan 29 2018

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[ArcTan[x]-Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 03 2011 *)

Prog

(PARI) a(n)=polcoeff(exp(atan(x))/(1+x), n)*n! \\ Jaume Oliver Lafont, Oct 24 2009

Crossrefs

Sequence in context: A354738 A073414 A085110 * A041229 A042887 A053908

Adjacent sequences: A013456 A013457 A013458 * A013460 A013461 A013462

Keyword

sign

Author

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

Extensions

Edited by Robert Israel, Jan 29 2018

Status

approved